Mario holds it in his hand and it releases flame, I think. However, sometimes, he can absorb its power- making himself stronger, but the Fire Flower weaker.
When he becomes Fire Mario, he absorbs the energy, and it changes his physical appearance, and enables him to shoot smaller fireballs.
However, in SSB, he only picks it up, and is able to shoot more flame, but it doesn't make him any stronger. That's my theory.