1. To advance to a position physically in front (of someone or something). The police cruiser moved ahead of the suspect's car and forced it off the road. He lagged around third place for most of the race, but with a dramatic burst of speed, he moved ahead in the last lap and won the whole thing.

2. To advance to a position of success, esteem, or accomplishment (beyond someone or something else). It's been tough watching my friends move ahead of me while I'm still stuck in this dead-end job. They were always seen as a second-tier tech company, but they've really been moving ahead in recent years.