The (double) blind pick is a way of choosing fairly what characters two (or more) opponents are going to play in a game.
For a double blind pick, both players have to pick their character without knowing what character the other player will choose. Usually this is achieved with each player telling an unbiased third party what character they will play so that the other player can't hear them. The third party then reveals what character each player picked.
Other ways of achieving the same result are also possible. For example, both players could write down their characters and reveal what they wrote down only after both finished.
The same system can also apply for teams, or when more than two parties are involved.
The main advantage of doing a blind pick is that character counterpicks are impossible. This is the reason why performing a blind pick is usually an option in a competitive/tournament setting, especially for the first game in a set. For other games in the set, the winner of the previous set usually has to choose their character first. The other party then is allowed to counterpick that character.