What is Super Mario 64 about?
Super Mario 64 is a classic tale of the Super Mario series: saving Princess Peach. Princess Peach invites Mario over to her castle for a cake she baked for him, but when Mario opens the door, Bowser informs him that he kidnapped Princess Peach, and imprisoned all of her servants using the power of the castle's 120 stars. Mario has to jump through paintings, which are the magic portals to other worlds in which Bowser's minions keep a close eye and guard on a single Power Star for each level in a painting. Bowser guards each level of the castle, and when Mario defeats Bowser the first two times, Bowser drops a key, giving Mario access to a whole other level to the castle. When you defeat Bowser the 3rd and last time, Princess Peach rewards Mario by baking that cake she promised him earlier in the game.
However, Mario's task is not done yet, as the castle has not regained all of its powers back yet, because Bowser had imprisoned all of the Power Stars.
In Summary: Mario must save Princess Peach from Bowser, and recover all 120 Power Stars needed to power the entire castle.