"Weapons" are, quite literally, weapon systems that spaceships in the game use. Compared to turrets, which is another kind of weapon system available in the game, weapons behave more like real-life guns. Their direction of attack is restricted to their mounted forward direction, which is most likely the forward direction of the spaceships.
Weapons are most commonly used by S-sized ships, and less used by M-sized ships (M-sized ships may equip some turrets instead). Rarely, they are even used in L-sized ships.