Terry's Nest is an area in Terrydactyland in Banjo-Tooie. It is at the top of the central mountain, and is the main theme of the world. At first Terry thinks that you stole his eggs, and will fight you. After you beat him, he will rethink and ask you to find his eggs for him.
Terry's eggs are located throughout Terrydactyland, but can only be hatched by splitting Banjo and Kazooie on the Split-up Pads and using Kazooie's Hatch ability. Find a few, Terry should reward you with a jiggy, find them all, he should give you another.
In some instances, after finding all of Terry's babies and returning after getting farther in the game, you can hear the chick's cries again but with no egg.