Damage is a term used to refer to when a Players' Humanoid's Health property is reduced by a script. When a humanoid reaches zero health the humanoid dies and all joints in the model are broken causing the humanoid to fall apart.
Damage can be modified by a script with an event that checks for the humanoid taking damage. This can cause taken damage to be reduced or even negated.
Types of Damage
Environmental damage is damage that cannot be configured in any way by a place creator. The only type of environmental damage that currently exists in ROBLOX is world border damage, which causes a ROBLOXian to die if they go too close to the skybox. The most common example of this is when a ROBLOXian falls off a brick into the bottom of the ROBLOXian world. After a few seconds, the ROBLOXian will die. However, the max distance a player can fall down can be edited by developers. The max is -50000, though by default it is -500.
Local damage is damage that can be caused by elements which can be modified by a place creator. Currently, only scripts can create damage. Local damage can be effected on humanoids by scripts by either applying the TakeDamage() method, or by manually setting a humanoid's health to a level lower than it was before. However, doing TakeDamage() will not damage the humanoid if there is a ForceField present in the character. If the health is set to 0 or less, the .Died() event will call. For example, say there was a character named Telamon within the workspace. To damage him by 50HP, we could either do this:
workspace.Telamon.Humanoid.Health = workspace.Telamon.Humanoid.Health - 50