To elevate or improve one's social, political, and/or financial position in life; to become more successful than one was before. You're only going to truly get on in the world if you make a point of rubbing elbows with those of a higher social standing. It's unsurprising how quickly Sarah has gotten on in the world—her tenacity and determination are matched only by her intelligence and talent. The Robinsons really got on in the world after they won the lottery.