There has been much debate over the title of the film & PTA has said repeatedly that it should be left up to your interpretation (along with the Frog Sequence & many other elements of the film). There are many Magnolia flowers (or paintings) scattered throughout the film. Here are Paul's comments on this topic:
"I always had the title of Magnolia in my head even before I wrote it," says Anderson. And the a couple of weird things stared to happen that verified the title for me. I did some research on the Magnolia flower. There's a concept that if you eat the bark from the Magnolia tree it can help cure cancer.
"There's no reference to it in the film," Anderson says in an interview with the online entertainment website, Mr. Showbiz.
"It's many different things: It's a street in the Valley. It's a flower."
Perhaps more tellingly, most of the women in the film have flower names, like Lily and Rose, but Anderson told Mr. Showbiz that if any of the characters represents "Magnolia," it is Claudia, the coke-fried basket case movingly portrayed by Melora Walters.
A key phrase that gets repeated throughout the film -- "we may be through with the past, but the past isn't through with us" -- is at the heart of the film's meaning, Anderson told Mr. Showbiz.