His career has had an interesting trajectory. When he first started out he just did meaningless, silly parodies of hit songs, often just building a song around a slight change to the title; "Beat It" became "Eat it," "Like a Virgin" became "Like a Surgeon," "Bad" became "Fat." As time went by, his comedy broadened out and he started doing songs that parodied the cultural zeitgeist of the time.
The first song he did this with was "Smells Like Nirvana," by far his best song ever. He really poked a hole in the grunge movement. I was a teen at the time, and it pains me to admit this, but I used to love grunge music because I felt like it "spoke" to me, even though I had no idea what anyone was saying.
After "Smells Like Nirvana," "Weird Al" parodied the cultural zeitgeist in songs such as "Headline News" and "White and Nerdy." With his new album, he has a song in "Word Crimes" which taps into the frustration many of us have over the ignorance of grammar in our society due to textspeak, among other things.