As you may or may not know, Banjo-Kazooie has a Stop 'n' Swop feature that allowed you to transfer some "hidden items" over to its sequel - Banjo Tooie. This was eventually canned due to technical reasons but was left behind in the game as a little secret that could be collected.
For anyone who cares, these eggs and the ice key don't do a thing and are just to collect them for the heck of it; however, if you are playing the 360 version, I believe they are used for something else.
Here is the list of cheats to access the eggs and ice key:
CHEATDONTYOUGOANDTELLHERABOUTTHESECRETINHERCELLAR
CHEATOUTOFTHESEAITRISESTOREVEALMORESECRETPRIZES
CHEATADESERTDOOROPENSWIDEANCIENTSECRETSWAITINSIDE
CHEATAMIDSTTHEHAUNTEDGLOOMASECRETINTHEBATHROOM
CHEATTHISSECRETYOULLBEGRABBININTHECAPTAINSCABIN
CHEATNOWBANJOWILLBEABLETOSEEITONNABNUTSTABLE
CHEATNOWYOUCANSEEANICEICEKEYWHICHYOUCANHAVEFORFREE