Floating-Point Operations Per Second
It's not video card related per se, but relevant to ALL processors that do floating-point calculations. Be it mega, giga, tera or teraflops.
With so many pixels on screen for gaming and physics calculations and advanced behind the scenes architecture GPU/CPUs need to be able to calculate more and more.
But I would never buy a GPU just because it says it calculates more xFLOPS than its competitor, there are more variables than just raw power.
Continuing from what Andrew said, it is a statistic for all processors, but of varying degrees of importance. GPUs need to be able to do a lot of math all at once, but very often it is relatively simple math, while CPUs need to do more complicated math, but less of it at a single time. This is also why Folding at Home runs faster on GPUs (when properly optimized) than on CPUs.
Right now, Andrew's point about purchases is correct, that FLOPS should not be determining what GPU you buy (unless you are doing specialized work, in which case you wouldn't have asked your question). In the future though, that may change as we get the next Playstation and Xbox hardware, so multiplatform games are not limited by the old, current generation specs. How far in the future is hard to say though, but my guess is over a year (possibly multiple years).