I have a magic bomb and I was wondering, what exactly does it actually do?

While you have it in your inventory, if you go to the Map to capture wild pets (Pets tab -> Capture Wild Pets), you will have a Magic Catcher to use. This guy is rather useful, since he can capture all types of creatures and is not limited to catching just Reptiles or Mammals or Birds, like the other catchers. 

My recommendation to new players - sell the bomb in the Item Trades. They sell relatively well there and especially at the beginning you can use the silver it brings more than a possible wild pet (in my opinion). I would say you are better off buying a nice pet from the pet trades which will make exploring and subsequent item and money gathering easier. 

Thank you! How much do you think I should sell it for?