A storm shield is a small metal shield that has an energy field generator built into it. The energy field is too small to be of much use against ranged attacks, but is very useful in close combat. A model that has a storm shield may take a 4+ invulnerable save in close combat, instead of its normal armour save. The save may only be used against one opponent per turn (the defender chooses who to use it against), and it may not be combined with a rosarius or iron halo save.
Errata — Chapter Approved: Codex: Space Marines Q&A (v3.0): A Storm Shield is not used to gain +1 Attack — it's purely a defensive item. It's on the single-handed weapon list (rather than under wargear) only to ensure a model can't take a pistol, a chainsword, and a storm shield all at once.