Thermoptic camouflage is, like most forms of camouflage, a way of protecting the user against being seen. However, unlike the camo in use today, thermoptic camouflage actively responds to its external environment. The basic idea is that someone wearing thermoptic camouflage is invisible to both optical and thermal sensors. Since this covers most of the useful ways to find someone (short of really sexy stuff like detecting air movement or using floor pressure sensors), it's a pretty handy thing to have. The basic idea, at least for the optical portion, is that tiny cameras sense what is on one side, and then some form of flexible display will show it on the other side.
The first fictional incarnation (known to me) of this technology was in Gibson's book Neuromancer, where a group called the Panther Moderns uses optical camouflage made of mimetic polycarbon for various forms of mischief and terrorism. In addition to protecting against surveillance, it had the ability to display backgrounds of the user's choosing, making it a bit of an art/weapon combo. They were called chameleon suits, and apparently had a limited reaction time; during one particularly chaotic scene, where hundreds of people were panicking in an enclosed space, the suits were unable to keep up, and began to produce "madly swirling shapes".
The major factor in the popularity of this theorized technology, including the name itself, is from Masamune Shirow's manga Ghost in the Shell. His version, used by government agents in Japan (and anyone else who has access to highly restricted military technology), makes the user quite invisible to optical and thermal sensors. However, it is very fragile, and if large amounts of particulate matter (water, dust, etc) is in the air, it is not terribly effective. Probably the most (in)famous use of this is in the Ghost in the Shell movie, when Major Motoko Kusanagi seems to strip naked and then become invisible. Of course in fact it was just a layer of camouflage that she was wearing under her armor; this is quite obvious when you see it rip and that her skin is a much lighter tone than the suit. As to the fact that this means her only coverage was a thin layer of plastic in a high risk area; well, she is made of titanium and carbon nanotubes, you know. In Stand Alone Complex when she is shown wearing camouflage it is colored a dark gray when off, presumably to avoid this sort of confusion.
The primary personal model of thermoptic camouflage in Ghost in the Shell is the Kyo-Re Model 2902, where 2902 means the second model built in the year 2029. Since a person (even a full body cyborg) can only carry limited amounts of batteries, this form of camo tends to have a very short lifetime, and is usually limited to covert operations. Equipment up to tank size is regularly equipped with it when necessary. No flying vehicles are shown using such camo; it's likely that between jet exhaust and the speed of movement it's more trouble than it is worth.
Another place this shows up is in Batman Beyond as part of Batman's suit. This was introduced half-way through the series, and functioned very much like the other designs. They had a specific term for it, which I forget; if someone who has the seen the series more recently than 2002 could remind me what they called it, I would appreciate it. Master Villian mentions that it also appears in the video game Deus Ex.
Optical camouflage, of a sort, actually exists today. Some researchers at the University of Tokyo have developed something which physically looks quite a bit like a piece of thermoptic camouflage that appears in Ghost in the Shell. From the video demonstrations, it appears to be a form of optical camo, though Wntrmute has pointed out that it requires the viewer to use special equipment (making it more a form of augmented vision than actual camouflage). The best thing about this project? In the references section, you will see "M. Shiro, Ghost in the Shell, Kodansya, 1991". You can find photos, movies, and descriptions of it at
http://projects.star.t.u-tokyo.ac.jp/projects/MEDIA/xv/oc.html.
DARPA, being the mad scientist types that they are, have also been working on invisiblity technology, but I can't find any good online resources on this. It's entirely possible that this project has been cancelled since I first read about it, as a large percentage of DARPA's projects end in failure (which is to be expected of an organization which takes on projects on the far edge of technology).