The Fireball is an attack that Mario can do from time to time. It is made of an orb of fire that can be used as a weapon or to destroy obstacles. Typically, the character can only shoot fireballs if they acquire a Fire Flower allowing Mario to become Fire Mario (Or Fiery Mario), which is what the original NES instruction booklet for Super Mario Bros. says.) However, some enemies can shoot fireballs without the use of a power-up. Additionally, Mario can train himself to shoot fireballs from his hand (without using a Fire Flower), which is evident in Mario & Luigi: Superstar Saga for the Game Boy Advance.
Super Smash Bros.
In the Super Smash Bros. series, Mario and Luigi's standard B move is a Fireball. Mario's Fireball bounces along the ground, while Luigi's Fireball (whose fireballs are green spectral flames) floats more through the air.