A frame, in the field of computer graphics (among others), is an instance of a screen display; it lasts but for a split second (hopefully), and when many frames shown in sequence, the human brain perceives the illusion of motion. This is the visual element of what allows film, television, and video games to be enjoyable.
A single frame takes a certain amount of time, and ideally, this time should be constant in order to preserve the illusion of motion (on older video game hardware, this was also necessary or at least highly convenient for keeping time at a constant!); because the vast majority of fighting games have their origins in the arcades of Japan and the United States, or take much inspiration from them, this “framerate” tends to be fixed at something like 60 or 30 frames per second (which essentially derives from the NTSC standard of displays, in a way). Thus, one “frame”, when used as a unit of time, can be thought of as, say, 1/60 second (which is not necessarily the exact value, but you can’t really tell, without superhuman ability, or a good timer and definite knowledge of how many frames are being displayed, or something to that effect).
In PC games, and perhaps in less primitive consoles and arcade hardware, the software may make a decision to drop frames (or delay them until they are ready to display) in order to preserve the game’s timing (or input/output accuracy, respectively). This is, of course, slightly undesirable because it doesn’t look good and doesn’t necessarily help gameplay, but it is a necessary evil at times.
Frames are often referred to in terms of “advantage” or “disadvantage” when it comes to throws, stun times, etc. for which speed is very much of the essence. For example, a 1-frame throw is ready to work on the very same frame the input is finished registering; anything else will be slower than that.
Frames in particular become highly important to be aware of; if you put out a move whose recovery leaves an opening big enough that an opponent has enough frames to start up a move, you will be a victim of a guaranteed counterattack.
Among the super special moves out there, there are moves that are not possible to block or otherwise evade after seeing the super flash, but this is due to a certain number of frames (differing from game to game) where all action is suspended.