Need help understanding 爱慕虚荣
虚荣 is a noun as well, meaning vanity. Now it's easy to get what 爱慕虚荣 means -- pursuing superficial things. 爱慕虚荣 sounds more literary. When referring to the character of a person, it is fine to say both 她是一个爱慕虚荣的人 and 她是一个虚荣的人. Both are common. The choice of the word also depends on the actual construction of the sentence. If there are other two-character words used in parallel, such as "他虚荣,自负,贪婪", in which you wouldn't want to use 爱慕虚荣 because it'll break the (sort of) rhythm of the sentence.