Starting with the poster for the movie, roses are all over the place in American Beauty. In fact, they're even in the title, since the American Beauty is a type of rose. But the question is: why?
Well, let's track where we first see the flowers in the film: when Carolyn is outside gardening. As Lester tells us via voiceover about his stifling, boring life with his super image-conscious wife, we see Carolyn busily snipping roses off her bushes. Later, when the Burnham family is having dinner, we see roses (presumably from her garden) neatly and tightly bunched in a vase in the center of the table.
For Carolyn, beauty is all about creating an image of perfection, and the way she treats the roses totally conveys that priority: rather than leaving the roses to grow naturally on the bush, she clips and arranges them in her very rigid, precise way.
There's a metaphor here for the passion—or really, lack of passion—in the Burnham household. Lester makes a big deal of how dead and sexless his life is, and when Carolyn later interrupts some potential sexytimes between them to make sure he doesn't ruin the couch, you can see a glimpse of how her obsession with perfection (which is totally at work in her obsessive gardening and florist tendencies) has interfered with life.
Knowing all this, we can interpret that early shot of Carolyn aggressively snipping roses off the bush as a metaphor for how she manages to "snip" other things out of her life—like passion. Actually, the rosey snip-snip is pretty solid metaphor for castration—and after all, we see Carolyn hacking at the roses just after Lester's comment about how masturbating is the highlight of his day (which, along with other stuff, suggests a less than active sex life with Carolyn). Hmm . . .
When Lester meets Angela, though, everything changes for him—and the rose motif changes with him. Once his passions have been aroused, suddenly we see a lot of free-flowing rose petals, all in fantasies of Angela.
In these visions, there are petals flying out of Angela's shirt (in a manner that mimics Lester's presumed ejaculation at the basketball game), petals coming out of Angela's mouth when he's kissing her, petals in a bathtub where Angela is waiting for Lester so they can canoodle, and of course, petals dropping on Lester from the ceiling as he watches a naked Angela recline in a huge bed of them (this is also one of the famous promotional images of the film).
Basically, roses = passion in American Beauty's universe, and the movie's presentation of the flower changes according to what stage Lester is in during his whole life overhaul.