Level 5 and above CPUs in the original Super Smash Bros. will never use the Fire Flower against Fox or Ness since Fox can reflect the flames and Ness can absorb them. Instead, they'll throw the Fire Flower at them.
In Super Smash Bros. Brawl, Fire Flowers, like all shooting items, can now be used while walking. 
Once you grab this item, press and hold down the A Button to make the flower breathe flames until its power gives out. The Fire Flower is incredibly useful when you want to push someone off the edge of a stage. In Super Mario Bros., it transformed Mario into Fire Mario, changing his garb and enabling him to throw fireballs.
A flower that breathes flames when you press and hold the attack button. The flames don't last forever, though--after a while, the flower will lose its fiery power. You can also throw Fire Flowers at enemies to set them on fire for a brief moment. In Super Mario Bros., Fire Flowers were used to transform Mario into Fire Mario.
Super Mario Bros. (1985)
Super Mario Bros. 3 (1990)
In Wii U
This Fire Flower won't transform you like in the Mario series, but it will still let you unleash some fiery damage! Holding down the attack button lets you spew fire at your opponents, dealing constant damage to them. You can also throw it at them, but it just doesn't look as cool that way.