When you mash something, you crush it. You might, for example, mash a marshmallow by stepping on it.
Recipes for banana bread almost always include an instruction to mash some bananas — in other words, you need to squish and press on them until they no longer look like bananas. A bully might mash your carefully constructed sandcastle, crushing it down to the beach. The word mash seems to be related to mix, both probably rooted in the Proto-Indo-European meik, "to mix."