The biggest difference is being 3-D. No more side scrolling for Mario. Left to right? How about left, right, up, down, up-left, up-right, etc? More movement, more freedom. Bigger levels, bigger obstacles. The Mario world changed greatly with new levels, looks, gameplay, and a whole lot more.

Other than the aspect of 3-D, there were some other changes to the Mario series. For example, Peach's Castle. Now, in most games, Peach has a castle, whereas before, she was always in Bowser's Castle. Nearly in every major Mario title, there's some point where Mario is in Peach's Castle for some reason. It created a new main feature for the series

Some other examples would be the Power Star, Princess Peach's name (She was originally Toadstool, but this was the first main Mario game to feature her name as Peach; the first was Yoshi's Safari for the Snes), Red Coins, Wing/Metal/Invisible Caps, etc. All new additions which now frequently appear in the Mario series and will most likely continue to be in the series

Visually, there's a big change, which is no surprise. From little pixels to a full fledged character, the physical change is obvious. Audio changes occurred as well. Koji Kondo, the music guy for the Mario series, did a great job for this game. Songs like Bomb-Omb Battlefield or Dire, Dire Docks are now classics, beautifully arranged. Just more examples of how Mario's titles have evolved from 8-bit to 64-bit to now.

New things were introduced to the Mario series, most of which still are in the Mario series. Great additions. Super Mario 64 itself also changed Mario visually and gameplay wise for the better, a mark of a truly great game. Nothing has changed the Mario series since, and until then, Super Mario 64 remains the most revolutionizing Mario game out there