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 go up 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 gone up in the world—her tenacity and determination are matched only by her intelligence and talent. The Robinsons really went up in the world after they won the lottery.