1. In baseball, to get a hit every time one is at bat (resulting in a batting average of 1.000). The slugger is still batting a thousand after a record eight at-bats.
2. By extension, to be successful in an endeavor or in multiple areas of one's life. I'm really batting a thousand this week—I got an A on my exam, I got the lead in the school play, and I won the poetry contest!