Eye candy is a term with a general meaning and a couple of specific meanings.
In the general meaning, it is an analogy with sweets. Candy is tasty foods of immediate appeal but no lasting nourishment value. Eye candy is anything which is visually appealing but of no consequence; fun to watch but not important. I guess you could put pretty shiny things and fireworks in this category.
Sometimes this is a reason to watch a movie which you know has no redeeming narrative qualities, but which you expect to look good. You might, for example, say David Lynch's Dune sucks as a movie, but it's great as eye-candy.
The first specific meaning is as an euphemism for sexually attractive members of the appropriate gender – implying that the people are very watchable but you are not going to get to know them better. E.g. there was plenty of eye-candy on the topless beach or check out the corporate eyecandy in that booth!
The second specific meaning is a geeky one, that of software that generates abstract colourful images on the screen which are watchable, but don't represent anything concrete.
Examples of this are programs such as Acidwarp, Cthugha, Mandala and aestesis. Some screen savers qualify as eye candy, especially the ones complex enough to warrant the mocking title "screen exhauster". Often colour-cycling is used. Often there is a strong central focal point, with rotation around or movement into or out of this focus.
The secondary meaning of candy may be an influence in this usage, as much eye candy is either reminiscent of psychedelic visions, or looks even better under the influence.
This genre of program had its heyday (its limited niche more like it) in the 1990s, when processor power was available for a motivated programmer to make eye-candy in his spare time, but before the rise of MP3s. Fractal images were popular in the early nineties. They were new and cool, and the processor power necessary to generate them relatively quickly had arrived.
Since the late 90s, the role of eye candy provider has largely been taken over by visualisations, effects and pluggins for music software such as WinAmp and Windows Media player. Despite the corporate backing, synching to music and, in many cases just being better due to more available processor power, eye candy is still much the same, and is still beloved of tripping geeks.
Eye candy is often projected onto screens at raves. In this setting, a VJ may mix eye-candy generated on the fly with pre-generated computer animation, movie footage and even homemade video onto the screen. As with a DJ the artistry lies in the selection of source material, the sequence in which it is presented, and in the overlaying of different video streams.
Precursors of this kind of eye-candy are the lightshows that hippies would put on at happenings and psychedelic rock concerts (Early Pink Floyd being particularly famous for this), and the humble lava lamp. You will see examples of this kind of effects in the movie Barbarella.
Eye-candy style sequences can be found in many movies, when the director wishes to convey something abstract, out-of-body, transcendental, cyber or just weird. Spaceships travelling through hyperspace or being sucked into a vortex wormhole are quite common examples. See also the end sequence of the movie 2001: A Space Odyssey or the opening credits for Doctor Who (2005 onwards).