Why/how can mockingbirds imitate other birds and sounds?

This is not a trait of only mockingbirds. Many birds can imitate sound. That is why parrots talk, they are simply imitating the sound of humans. I have a stellars jay, that makes the call of a red tail hawk when coming into the yard. It clears the feeders of all small birds for a short time.

Mockingbirds Sounds

The reason they are called mockingbirds is that their brain allows them to mock or copy other sounds, especially bird sounds.

Perhaps they are still getting song info (genetically) from a time when they were related to other birds.