Why can parrots talk? We're talking physiological here. Please explain.

All birds can talk. What you are asking about isn't talking, it is mimicry, the fact that the sounds the parrots make sound like human words.
Parrots are very intelligent birds, but are not the only ones who learn how to mimic. Birds learn how to mimic other birds to confuse them, as a starling would when it is going to lay its eggs in the nest of another bird, it calls to the other birds to find out where they are.

It was a matter of evolution, where their tongue is attached and such, but do not think of it as talking, it is simple mimicry

I would submit that there are four reasons some birds, such as parrots, can "talk."

They have excellent hearing and can distinguish between different sounds very well.

They have a specialized and well-developed vocal apparatus, capable of producing a wide variety of sounds.

They are quite intelligent, and use the sounds they produce for specific purposes, rather than just to make noise. Because of their intelligence and resulting ability to learn, coupled with their vocal capabilities, they produce sounds that are useful for any number of reasons. The parrot does so because people respond to it accordingly. The bird knows it is imitating human sounds, and easily sees the favorable attention garnered from mimicking those sounds.

But also, birds seem to enjoy a social element to their existence. There are two operative words to that statement, however, not just the fact that they are social animals. They also exhibit enjoyment. Anyone who has watched birds in flight for any length of time, will have noticed that they sometimes seem to do things just for the fun of it.

Yes, they mimic because they can (hearing and vocal capabilities), and because they are bright enough to manipulate their abilities. But their mimicry is not simply mechanical, or reward-based in a psychological conditioning manner. They also appear to actually enjoy it for their own sakes, not just to attract attention. They don't know "what" they are saying, but they like to repeat certain patterns--to "say it" nevertheless.

Excellent, Brvtvs! You caught on when I said physiological. Not Psychological! Good job!