The basket shows various information regarding a person's collection statistics, their hatched and incubating pets, and potentially a nest. If the basket being viewed is yours and you have not collected many eggs in the current season, an information box will show with a link imbedded tutorial video.
If the owner of a basket has collected many special eggs or hatched many pets, you will need to click a link in either section to show all the special eggs collected and hatched.
Note: When you find an egg, you will be offered a chance to add it to your basket. This does not directly take you to your basket, but instead to a option page. See collecting and basketing for more information.