Pellets are an extremely important part of a birds diet, and should make up a majority of most birds' diet. Pellets offer a nutritious, convenient food source for your pet bird.
Compared to seed, pellets are a no brainer staple diet. Pellets are far more nutritious than seed, significantly less fatty than many seeds, and the entire pellet is edible compared to just the "germ" (inside) of the seed with the hull being discarded to your floor.
Compared to fresh foods, pellets do not spoil nearly as quick, one pellet can offer the same nutritional range as a half-dozen fruits and vegetables, and are less messy overall.
This does not mean that vegetables, fruits, and seeds are not a good thing to include in a bird's diet. They certainly have their place. But, pellets are an ideal staple food for most parrots.