ITB stands for "International Tie Breaker." When a softball game is tied at the end of six innings, the International Tie Breaker rule goes into effect. At the start of each inning, a runner is placed on second base with the intent of accelerating opportunities to score and bringing the game to a speedier conclusion. The runner is the last batter to make an out in the previous inning. At least one full inning is played, allowing each team the same chance to score. If the score remains tied, the same process is used in each inning until a victor emerges (one team scores more runs than the other at the end of a complete inning).
There is also "Progressive ITB" in which runners are placed on second AND third at the start of the second (and subsequent) extra inning. This is not an ASA rule but is used in some tournaments. The runners are the last batter to make an out plus the person batting immediately before that batter.