What does bitcoin actually do with these problems? I understand this might be a simple question but what do cryptocurrency companies do with these problems when you mine. I know you get reward for solving a problem but what will bitcoin do with that?
Contrary to popular belief, mining is not actually solving any problems. There are no math problems that miners are working on to solve. Rather what miners are doing are just hashing data and then seeing if the resulting hash is less than a given target which everyone can calculate independently with data from the blockchain. The work that they are doing is only for securing the Bitcoin blockchain; it is not useful for anything else. So they aren't solving puzzles or problems, they are just doing work to make the Bitcoin blockchain secure.