1. Not the proper match for someone, often because the other person is considered superior in some way. Although it can be used in other situations, this phrase is very often applied to romantic partners who are more attractive or wealthy. I can't believe that average-looking guy is dating a supermodel—she is totally out of his league!

2. Not within the scope of one's training or skills. I've only been working in the department for a few months, so that management position is really out of my league.