Fuego, for clarification, I'll give you an example.
Player 1 vs Player 2
Round 1 usually involves people picking their mains, or, in certain cases to avoid counterpicking (catering to a bad matchup), a double blind can be called, where one player tells a third party who they are going to use, and the other picks their character, while the other player picks the character they said they'd use to the third party.
Player 1 wins.
Round 2: Player 2 can now pick a stage. Player 1, once learning which stage is going to be played, can choose to change his character or stay. Player 2 can choose to change his character or stay AFTER Player 1 has decided (hence, counterpicking)
This happens again if the set count becomes 1-1, and it then becomes Player 1's counterpick.
There is the option of Random counterpicking, which involves the losing player saying "Random." This forces the winning player to stay the same character, and the stage is randomly chosen by the game between the 5 neutrals.
There you have it, counterpicking.