Bombs contain chemicals which will mix and produce an enormous amount of heat very suddenly. Hot materials take up more space than cold ones, so the swelling of the chemicals bursts open the casing of the bomb, flinging pieces of metal about, as well as sending out a huge shock wave.

Bombs need a detonator to set the chemicals working. The detonator is in the nose, and that is why bombs are designed to fall nose first. If the detonator does not work, the materials in the bomb will not explode. This is why you sometimes get unexploded bombs.