You have the ability to achieve anything you want.
Finish graduate school and the world is your oyster.
Webster has a definition for oyster that is a bit obscure and certainly fits the phrase: Oyster - something that is or can be readily made to serve one's personal ends.
Oysters produce pearls, objects of great value. Once you have the oyster, it gives up the pearl without much of a fight. Getting the pearl requires the oyster to be opened. But despite the hardness of the oyster shell, they can be opened with ease. Oyster shells are held closed by a single muscle called the adductor. Oysters are shucked (opened) using a thin knife to cut the adductor muscle. Once the adductor is cut, the shell falls open.
If the world is your oyster, then it is a place where you can get something of great value with ease.