A corner combo is a term that can only be done in the very edge of a map (corner) in Street Fighter games.
As every Street Fighter game has a boundry to the left and right side of the stage, there is a limited amount of space available to each character. When the corner is reached the character in that side of the corner can not move into that direction anymore. This also means that characters backed into a corner can not be pushed back further by attacks either.
Corner combos tend to do more damage than regular combos. Pushback on hit and block is lessened as one character isn't moving back, meaning more attacks can be linked in a single combo. Juggles do not have to worry as much either, meaning that attackers can further tack on attacks as the specific juggle rules of the game would allow. The benefit of corner combos vary from character to character, as some can simply link another attack while others can add multiple hits to their standard combos.
While not combos some characters can benefit from the corner in other ways. For example from World Warrior to Champion Edition Zangief had a change where the distance between himself and his opponent after a successful Spinning Piledriver is much greater than the previous game. However if Zangief himself is in the corner and successfully performs his grab he will be much closer as he moves further from his opponent than his opponent does from him when he jumps back, and the corner will not allow Zangief to distance himself nearly as much.