Explosions are rapid outward bursts of energy that do varying amounts of damage. They range from macroviral explosions that destroy only the targeted bug, to Bleeprin-Purple Stuff explosions that may or may not take out a wall, to the supernova explosions that consume Suvian star systems.
They are usually caused by chemical or nuclear reactions. Common causes among the PPC include botching Stuffs, mixing extra-canonical substances into magic potions, the launching of missiles at Suvian targets, or simply belting a 'Sue with a heavy piece of legendary goodfic.
They can be good things or bad, depending on your intentions, proximity, degree of shielding, level of sanity, and the force of the explosion in question. Explosions are also very shiny, which is generally considered a good thing.