Types of Explosions
Any explosion that is the direct result of using a weapon; such as a sword laden with explosive magics, or a gun that's been given explosive bullets. The most obvious example is a grenade or a block of TNT. Most guns can be put into this category, given the common firearm mechanism of propelling a bullet out of the gun's barrel through an explosion in the chamber.
A larger scale example would be the atomic bomb that a player can detonate on the town of Megaton in Fallout 3.
Think Final Fantasy or Dragon Warrior for magic-based explosions in games. Spells such as "Flare" in Final Fantasy and "Explodet" in Dragon Warrior are good examples.
In other games, a character may motion with their hand to create a fireball or a beam of powerful light, which will explode upon impact. In Oblivion, the magic-wielding player motions forward with his/her arm and points to create a fireball, which then hurdles through the air, exploding upon any solid surface.
Magical "summonings" also create magical explosions, such as Bahamut's attack in most Final Fantasy games.
These explosions emanate from the world around the player. They can activate on their own, or be triggered by the player's actions. Classics, such as the exploding barrel and fuel tank are often large and loud explosions - and in some environments, they can connect with other exploding objects to create a chain-reaction.
This also contains objects such as vehicles, booby traps, and mines. This type of explosion can be very important to some games, as explosive environmental objects are often part of objectives or checkpoints in a game.
These explosions are the result of any living thing that is able to explode. A simple example of this would be any kamikaze enemy in a game that's willing to run up to a player and detonate themselves.