What does training mean in The Hunger Games?

Answer 1

All of the tributes for each district participate in a brief training period. They work with a mentor & select the best approach for the games--ideally, one which plays to their strengths. Technically participants aren't supposed to do any long-term training, although certain more affluent districts violate this rule and prepare their children for the games. Those tributes are referred to as "careers" in the book.