In Super Smash Bros. Melee, the Screw Attack alters a character's first and second jumps, changing them to mimic Samus' trademark move. If thrown at an enemy, they will be knocked upwards in a Screw Attack, dragging any nearby opponents (even the thrower) into the attack. They then fall down helplessly. Many players use this in a sort of pseudo-combo with Samus' Up Special.
In Super Smash Bros. Brawl, the Screw Attack is a badge item, similar to the Franklin Badge and as a result, can no longer be thrown but allows the user to attack as normal, having their ground and midair jump being screw attacks as originally (Only the first midair jump if a character has more than two). The badge can be worn at the same time as the Franklin Badge, and will eventually fall off. Most, if not all of the attack when jumping has IASA frames, allowing for the ability to cancel the attack into any one of a character's aerials or specials.
One of Samus Aran's power-ups from the original Metroid, the Screw Attack turns a jump into a rotating attack move. When carrying this item, any character's ordinary jump move will turn into a Screw Attack. By the same token, if you throw this item at an enemy, your foe will spontaneously do a Screw Attack.
A badge you can wear to turn your jumps into Samus's signature Screw Attacks. In Super Smash Bros. Melee, it was an item you carried, but this time around it's a badge you wear--which means you can use it and another item at the same time. There's a good chance you'll be able to string together Screw Attacks and midair strikes for powerful combos.