The phrase "to move up" means to advance or progress in a particular field, position, or rank. It can refer to someone's career, social status, academic achievement, financial standing, or any other area where there is room for improvement and growth. To move up implies that an individual has worked hard, demonstrated their skills and abilities, and been recognized for their efforts, resulting in a promotion or increase in status. It can also refer to the act of moving from one level or position to another higher one.