It is very effective against skeletons, as it deals crushing damage, unlike a sword.
It is destroyed by piranae in Comic #86
The Hammush was added into Terraria with version 1.2 after Redigit decided to add in a Legend of Maxx reference.
He gets it from when Cyril (known so far as "Guidey") goes to find food in the cave (comic #71) and leaves the Mushbrella to stand (it falls off then he comes back with no food and holds it up). After, when Maxx wakes up, and starts arguing about weapon failure. Maxx then theorizes that the wooden sword deals slashing damage and not crushing damage (comic #74). Next, after going on that speech, he realises Cyril is still holding the Mushbrella and (soon) turns it into the mighty Hammush.
The Hammush's name comes from combining the words hammer and mushroom.