过上 = 过 (to live / spend [time]) + 上 (resultative complement marking 'achieving / getting into a state'). Almost always followed by 日子 / 生活. It carries an implication of reaching a desired or new condition - you don't 过上 a bad life unless ironically.
grammar
上 here is a resultative complement showing successful attainment, as in 爱上 (to fall in love), 喜欢上 (to come to like), 当上 (to become [a position]).
