Annihilation is the total destruction of something. In World War II, our nuclear bombs resulted in the annihilation of Hiroshima.
If you spill milk on your textbooks, it won’t result in annihilation — this word is much more serious. After an annihilation, there's nothing left but total, horrific destruction, like a wild fire completely wiping out a forest or a tsunami sweeping away a seaside town. This word has an end-of-the-world feel to it: many religions have stories of annihilation of some sort, resulting in the end of everything.