Super Mario Galaxy is an 3D platformer about collecting stars and exploring new galaxies with stars that you have collected from the galaxies ,the big differences here than past Super Mario games is that this game has a wide variety of worlds to explore and is built around the main premise of gravity .
Another main thing that seperates this from other Super Mario games is that there are prankster comets which are much harder variations of the original level, also this game has more fluid movement and controls than the previous games.
One of the big features of Super Mario is the gravity premise, with the game constantly finding new ways to do this with levels that switch the gravity, and levels that allow you to skip sections if you are good at using these mechanics.
The wide range of galaxies and stars allows for a unique experience, with many featuring new powerups such as the ice flower that allows you to walk on water.
Or if the game is a bit too easy for you, you can try the prankster comet levels which some of them increase the difficulty hugely and most of them are timed making you get through the level as quickly as possible.