Definition of corner flip
A 50%-50% situation. The term coin flip refers to a coin. If someone tosses a coin in the air and asks you if the coin came up heads or tails and hides the result, you have a 50% chance of getting the right answer. This is the metaphor that is often used to refer to a game that has a 50% chance of success or to refer to an all in with 50% preflop equity.
Additional details on the flip corner
If a player is talking about a corner flip, he will often mean a hand that was all-in preflop with 50% equity. The classic example of a corner flip is when a player calls all in with AK and his opponent has a pair. If we want to be picky, we would say that the equity of the hands is not exactly 50%-50%, but that is what is meant by a corner flip. The two hands will have roughly 50% equity each. Sometimes you won't have the choice to take corner flips. Imagine you are in a tournament and you have a small stack, say 5 blinds. The players have all folded until the small blind pushes all in (again). You look at your cards and find a pair of 5's. Your opponent will almost always have 2 cards higher than your 5 for a 50% equity. You will then say that you took a flip to amass chips.