Technically: What is a Cinemagraph?
Cinemagraphs blur the lines in more ways than one when it comes to defining the term so I've decided to dedicate an entire post to explaining what I consider to be 'technically' a Cinemagraph.
For an in depth look at the difference between cinemagraphs and gifs read my earlier article: "Game Over Gifs".

This is purely a 'technical' look at what I define as being a cinemagraph. I'm not looking at the broader term and what it means from a consumer perspective. It's like the specialty tea business I also work in (yeah I happen to be a tea expert). Tea from a consumer perspective covers just about any herb, leaf or fruit that's infused into hot water, but technically in the industry we consider 'tea' being that which comes from the Camellia Sinensis plant i.e. black, red, green, white, yellow, oolong tea and puerh. One might argue that at the end of the day it's the general consumer perspective that matters but it doesn't mean we can't define parameters as creatives and as an industry which may help to guide consumer perception in the right direction.
I produce two different types of work and I refer to them differently.
1.) Motion Loops
2.) Cinemagraphs
MOTION LOOPS
Let's get this one out of the way first because this falls into the category of NOT a Cinemagraph. Motion loops can encompass a broad range of techniques. From an animated gif produced from a movie, cartoon, home video or computer graphics. Technically if it's a regular video set to replay in a loop or a .gif then it's a motion loop.
However what I'm talking about there is a video which has been edited to seamlessly loop so you can't see where the end loops back to the beginning again. This method allows for a video or gif to auto loop as a background image on webpages, digital screens (i.e. as an artwork in a digital frame on your wall) or social media for as longs you like. The fact it has no jump each time it loops makes it particularly stunning for artistic photography such as landscapes (waves on a beach, waterfalls, trees blowing and clouds in time-lapse) or cityscapes (time-lapse of cars at night etc).
There is no masking required for these, Except I might occasionally mask an area of the video to be static which doesn't loop as seamlessly. However the difference here is that it's barely noticeable... a Cinemagraph as you'll see next has an element of the video which the mind clearly expects to be moving but is not.
I mostly use the Flixel Cinemagraph Pro software to create motion loops as well as cinemagraphs because it allows me to very easily create the crossfade or bounce loop and export the 3 second repetition into a 30 second or 1 minute clip with a few variations on the crop or applying a quick filter for black & white etc before uploading it to my cloud hosted Flixel Gallery where they look fantastic looping in high res. There's still no better way to embed looping video than what Flixel offers. Although I've created some of these simple motion loops with the Flixel software and uploaded them to my Flixel gallery I wouldn't technically call them Cinemagraphs and I'll usually type 'Motion Loop' in the description.
The following shot is where the two start to crossover... there's nothing obvious that tells the viewer that it's a Cinemagraph such as the silhouette of a figure captured leaping across the sun... but you'd also soon realise that the sun never sets, it just sits there as the grass blows wistfully in the foreground. Is it a Cinemagraph or a motion loop? If I'm really stringent on myself I'd call it a motion loop because the sun remaining still is just not obvious enough to 'most viewers'.

CINEMAGRAPHS!
A Cinemagraph in it's broadest sense appears like a still photo with isolated areas of the image moving in a seamless loop.
To be called a Cinemagraph there should be at least some part of that isolated motion that has been captured as true video within that scene (or timelapse being a series of still photos joined into a video first).
The area that has been edited to remain motionless should be obvious enough that the mind of most viewers would expect it to be moving.
This second point is important and where the line between a Cinemagraph and a motion loop often blurs. I often create a Cinemagraph that isolates an area of motion in the video while the rest remains still... such as some trees that were moving in the background. But sometimes you'll be forgiven for thinking there was no breeze that day and the trees were just very still... so it doesn't have the desired impact of a cinemagraph. Technically yes you can call it a Cinemagraph because 'you' know it is but if nobody else realises then it's basically just a motion loop.
CROSSFADE OR BOUNCE LOOP?
Whether it loops in a seamless crossfade or using a 'Boomerang' like bounce back and forth doesn't matter either... while the subtlety of a smooth crossfade is normally preferred by the top Cinemagraph artists there are times where the playful bounce loop can work perfectly to bring some magic and fun into a Cinemagraph. Again... what makes it a Cinemagraph is the combination of motion and still elements which is why loops made with the Boomerang app are not cinemagraphs. The following is a great example of this from my friend Jimmy in New York. On first glance you think it's using just a bounce loop but if you look again you notice he's cleverly used a crossfade loop on the smoke coming out the guys mouth. I also love the fact he's used real fire (apparently using a technique combining water + dish soap + butane! Youtube it).
This brings me to the next important point... adding motion elements like fire in post...
ANIMATED PHOTOS vs CINEMAGRAPHS
This is where we will get some debate! Personally I only class something as a Cinemagraph if at least one element of the isolated motion loop comes from original video material. Motion added using effects such as CG objects, pulsing light flares, other graphic elements or overlays is an animated photo, not a Cinemagraph. I use these often in my work too but I try to combine them with at least another element that was original motion in the video. However overlaying video (either your own or stock video) to create motion is another blur of the lines... because it's motion that has come from true video motion I would argue it then brings the edit into being a true Cinemagraph when it's added as an overlay. The following Cinemagraph has real steam from a stock video I purchased for $9 added as a slow motion overlay, but the fans above are the real fans from the original video of this scene. If it was just the steam it remains debatable but I'd still lean toward it being as Cinemagraph!

Plotagraph is software which has gained popularity and produced some amazing results using a morph technique on multiple points of a still photo to animate it into a flowing effect. It works nicely on clouds, steam, flowing water and hair but it soon becomes fairly obvious which images popping up on Instagram are done with software like this. They're popular because people can take existing photos and animate them rather than having to go out and shoot original material specifically for a Cinemagraph. That makes it a more cost effective option but like anything with a low barrier to entry it's very quickly spreading... and like a quick and catchy song on the radio I don't see it having the longevity compared to a premium format like cinemagraphs. Because of a more specific workflow from capture to post production, Cinemagraphs have a much higher barrier to entry. Therefore those who do cinemagraphs well will truly stand out... be they brands or photographers.
The following image is perhaps the second Cinemagraph I ever made... that's a few years back now! It shows a typical Cinemagraph... your mind tells you she would be moving if even slightly so on first glance it looks like a photo, then you notice the noodle being sucked up and wiggling like the worlds longest noodle!

DESIRED IMPACT
A Cinemagraph should elicit a reaction from the juxtaposition of seamless repeating motion within the appearance of a still photo.
I say 'appearance' of a still photo because technically you're saving it as a video and it's being auto-played and auto-looped online without video controls showing (or on a digital TV/Billboard)... so it appears like a photo on your screen until you notice it actually has something moving within it.
A GOOD Cinemagraph will not only elicit a reaction from this appearance of motion in a still photo but it will work as a good image in it's own right, even if it were to stand alone as a still image with no motion. The motion element should help to elevate it's impact as a good image in some way rather than act as a gimmick or trick for the sake of adding motion.
That's all easy to say... but of course not every Cinemagraph has to be the perfect Cinemagraph, I'm constantly experimenting and not all of them meet this stringent criteria!
MAKE THE RULES TO BEND THE RULES!
I set my own rules then I bend them to push myself further to the limits (without actually breaking them). I don't want to set limits on my creativity but I like to set limits on a definition and a format such a 'Cinemagraph'. Why? Because it helps to maintain some separation from all the other formats and techniques out there such as gifs, boomerangs, live photos... which are too often called cinemagraphs as the popularity of cinemagraphs rises. The problem with that is that it devalues what I and so many others do because for the most part these other definitions refer to quick and fun techniques where cinemagraphs are a more professional and high end format which takes much longer to create in post production.
Cinemagraphs started as a high quality professional format by the New York team of Jaimie Beck and Kevin Burg who coined the name and brought about the techniques popularity and which has been championed as a professional format by Flixel who made the first dedicated Cinemagraph software.
Let's keep it on track! ;)