The pickaxe is given to you by Rosalyn at Star Level 3. It is used to break rocks that have fallen in the way of paths or entrances. It is also the only way to gain access to the desert. Pickaxe's also appear in MySims Kingdom where they can be used to start mining after obtaining it from Elmira. She seems to regret giving it to you afterward.
Entrances[]
Using a pickaxe to destroy the rocks blocking the entrance to the Desert