The lovebirds are a symbol of love.
We suspect you could have figured that out.
Whose love is also pretty easy to figure out. Melanie and Mitch argue about the lovebirds right at the beginning of the film, and then Melanie delivers them to Mitch in Bodega Bay. As Lydia says when Melanie tells her she brought Mitch lovebirds, "Oh, I see." Melanie even wears a green suit throughout the film, mirroring the green lovebirds.
The lovebirds are a great excuse for Mitch to flirt with Melanie:
MITCH: Well, uh, these are for my sister, for her birthday, see, and uh, as she's only gonna be 11, I, I wouldn't want a pair of birds that were ... too demonstrative.
MELANIE: I understand completely.
MITCH: At the same time, I wouldn't want them to be too aloof, either.
MELANIE: No, of course not.
MITCH: Do you happen to have a pair of birds that are ... just friendly?
The flirtation isn't what it seems, though; turns out, Mitch recognizes Melanie from one of her court appearances and probably has no intention of starting anything up with her at this point. He thinks she's a spoiled, rich party girl. The lovebirds are for his sister; that's where his affections lie for now.
But, it's not just about love. The lovebirds carry lots of other symbolic weight.
They're caged, for one thing, and it's easy to assume at first that the other birds are wreaking vengeance on their behalf against the kind of people who try to keep them and other pet shop residents locked up. Plus, they're the only birds in the film that don't lose their minds and turn into crazed marauders.
The lovebirds get a little agitated right before the chimney attack, but they stay inside their cage and don't try to bust out or peck anybody. They stay sane while the world around them, human and avian, goes crazy. We half expect they'd learn to open the latch of their cage, like those velociraptors in Jurassic Park …but they don't.
(And, how about that great shot of the birds in the car, leaning into the turns as Melanie tears along the winding coastal highway? Hitchcock pointed out that there's the sound of screeching tires during this scene.)
Do the lovebirds symbolize some kind of middle ground between the forces of nature and the forces of civilization? Maybe they represent some kind of normal world order, where birds behave the way they're supposed to. Cathy asks to bring the lovebirds with her when they sneak out of the house to leave town. She's not associating them with their radicalized feathered pals. In that way, the lovebirds symbolize some small hope for humanity, some hint that at least something in this world hasn't turned against them.
On the other hand, given what some critics believed about the importance of the "cage" motif in the film (See "Cages" in our "Symbols" section), maybe it just shows that the humans haven't learned a thing.
Yeah, it's probably that.