American Pie references the changes in popular music and culture following the deaths of Buddy Holly, the Big Bopper (J.P. Richardson), and Ritchie Valens in a plane crash in 1959– "the day the music died."
The cryptic lyrics borrow from song titles, artist nicknames, song lyrics and cultural events, and events in the songwriter's life, in a story that mourns the loss of innocence and growing disillusion among America's youth in the decade after the plane crash— basically, the 1960s as a whole.
There's debate about some of the references, and some seem to serve more than one purpose— covering multiple ideas with one image— but overall the meaning is known and can be followed.
Artists/songs/events mentioned (not exhaustive):
Marty Robbins
Sock hops
Elvis
Bob Dylan
The Beatles
John Lennon
Joan Baez
The Byrds
The rise of counter-culture
The Rolling Stones
The Manson murders
The Hell's Angels (and the infamous deaths at The Rolling Stones concert)
As I said, some of it is open to debate, and the artist probably did mean for some open interpretation, but the song is not without meaning:
link
But that doesn't mean that everyone singing along knows what the heck it's all about! (I had a teen friend who was convinced it was based on Revelation and the Apocalypse… and maybe in some ways it was. Allusions can go in many directions, all at the same time.)