FPV is an acronym meaning "First Person View". A person referring to "flying FPV" is referring to piloting their model aircraft from a first person perspective onboard. This is accomplished by means of tiny video cameras and wireless RF links. The typical FPV plane consists of many components that must work well together to get the job done.
The Plane can be anything from a stock run of the mill foam parkflyer, to totally custom purpose built "UAV" types. There will always be some debate as to what the "best" choice is for a FPV airplane, but the truth is, everyone's needs and expectations are different. There is no single best airplane for everyone. There is no denying though, that the Multiplex Easy Star is a great place to start. It's durable, flies well, carries the extra payload well, and there's TONS of information on the various forums. There's probably not a single question you could ask that hasn't already been answered at least once. Flying wing types tend to work well also. They are a bit more versatile and portable than the Easy Star. I've never personally flown one, so I can't really compare the two other than what I've learned reading the posts by those who have.
Here's some examples of typical FPV planes:
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The product tag cloud shows the different tags (keywords) associated with FPV flying products.