All explosive weapons (those that are of the HE damage type) are area-effect weapons: they do damage to all units and objects within their explosive radius. (The Small Launcher's Stun Bomb is also an area-effect weapon.) Incendiary munitions affect a circular area as well, but inflict damage in a very different way.
This damage radius is two-dimensional -- it will only affect units and terrain on a single level. Even a Blaster Bomb can go off immediately above or below a unit, and the unit will be unaffected. Since grenades cannot be targeted at any location in mid-air, this means flying aliens (and soldiers in Flying Suits) are generally safe from such attacks.
Area-effect weapons will apply their damage to the under armour of all units in a one-tile radius from the centre of the explosion -- i.e., a 3x3 area with the impact point being dead centre. The under armor of most units is weak, so area-effect weapons can be more effective than the underpowered direct-fire weapons available early in the game. For instance, they are the only effective way to battle Lobstermen if you haven't acquired Sonic weaponry yet.
All damage outside this 3x3 area is treated as normal directional damage -- so it is worthwhile to turn toward a grenade (and take it on the front armor) if you think you think you are within range of its blast.
Area-effect weapons can be very effective against large (4-square) Terror Units (UFO), (TFTD). This is because each square of the unit will take damage from the explosion, effectively quadrupling the damage dealt.