What can you do with the private key? I am trying to understand all security regarding blockchain and bitcoins. 

Let's say you have a bitcoin wallet which is secured, only you know the private key. This bitcoin address was created on one of the bitcoins wallet provided by bitcoin.org 
What if a person has your private key? I know it's difficult but let's say he knows the 54 letters private key from hacking a database. How can that person interact with your wallet? 
Does he have to know which wallet you use as well or can he use just the private key to 'log in'?
Anyone who knows the private key will have full access and control of any coins stored at the corresponding address. 

When you put a password on a wallet or login account, that password is only for unlocking that instance of the wallet (it is possible to create another instance, that is not locked by your password). Once unlocked, the wallet will use the private key to sign transactions that move the coins, etc. But without the password an attacker can not unlock the wallet if it the wallet alone is found. 

However, having the private key itself means you don’t need to unlock the wallet, because you already have the key. You can import the key into just about any other wallet software, and then use that wallet instance to move the coins, etc. 

There is BIP38, which allows you to password protect a private key itself, but this is different, and a less common set up.