ArmA itself is a sandbox environment, it comes out of the box with a variety of guns, vehicles, and not much else. Users create either Co-Operative or Player versus Player (you may hear the term Team v Team here) missions using the editor. The objectives of these missions are as varied as players themselves. You may find missions where you defend against endless waves of AI controlled soldiers, large scale conventional "Force on Force" combat between armies of players with vehicles, small special forces missions where you stalk and forcefully extract a High Value Target, or any other potential combat related task.

The community typically tend to mod the game to some degree or another. There are a variety of ways to obtain and install mods for ArmA such as the game's own launcher, external programs like PlayWithSix, or by manually placing the appropriate folders and editing the shortcut (not hard at all once you know the context!) Mods add new or modify existing content in the game. Some of the most popular mods right now are Red Hammer Studio's Russian and American forces mods which add detailed copies of equipment in use by those countries militaries, another popular addition is the AllInArma terrain pack which adds new maps (called Islands in ArmA lingo) for use in missions.

The game differentiates itself from the nearest potential competitor, Battlefield, with a focus on realism. Vehicles have individual components that can become damaged and require fuel for longer missions, night vision goggles are required to effectively function on dark nights, ammo pickups are not universal, more equipment on your person makes you less mobile, ballistic penetration is accurately modeled, many sights have adjustable zeroing and dual optics (4x magnified optic with a 1x close up dot mounted on top, you can switch between the two as necessary), etc.

tl;dr, you can do almost anything from 50 on 50 full scale conventional combined arms force on force player versus player down to 1-2 player versus a handful of AI.