The mayor was re-elected by a landslide majority.

re-elected 是动词 re-elect 的过去分词形式。re-elect 由前缀 re-（表示"再次"）和动词 elect（选举）组成，字面意思是"再次选举"。re-elected 表示"再次当选"。 landslide 本义是"山体滑坡"，这里用作比喻，形容选举中"压倒性的优势"。majority 指"多数票"。landslide majority 指"压倒性多数票"。