Suppose Player A and Player B enter a pot of draw poker, and both draw flushes. Now both players miss and go onto check after the draw. Player A has an ace-high draw, while Player B has a king-high draw, resulting in Player A winning the pot. Basically Player backs into winning the pot due to his ace-high draw.
So a when it is said that a player backs into winning a pot, that implies that s/he has won a pot with a hand, which in normal circumstances would have folded to any bet. Therefore, winning a pot unexpectedly, or even by default, can be termed as back into winning the pot.
Another example is, suppose Player A drew three cards, catching K-Q-J. Player A then passes after the draw, all set to fold if any other player bets. But unexpectedly, the three one-card draws pass, simply because the other players are afraid to bet, and have already paired, which means, Player A now backs into winning the pot.
A player can also back into a flush, while trying to make a backdoor draw. For example, if suppose Player A starts his hand with three cards of the same kind, but ends up making a runner-runner flush, he has now backed into a flush. Or even if a player ends up with a hand other than what s/he was drawing to, s/he can back into a flush. For example, suppose in a game of Seven-Card Stud, Player A starts out with a two pair, in the first four cards itself, then Player A will now back into a flush.