Moving Ether around is very easy, but in the background an important part of moving and storing Ether involves something called a ‘private key’. The easiest way to understand private keys is to think about an old-fashioned mailbox system:
Let’s say Maria wants to send mail to Peter. First she needs to know what Peter’s mailbox address or number is. Let’s say Peter’s mailbox is number 2034. Similarly, if she wants to send Ether to Peter, she needs to know his Ether address, which is a number that uniquely identifies him. This is also sometimes called his wallet address, or public key, which functions similar to your bank account number. It’s a long and complicated number because there are so many Ether ‘mailboxes’ in the world, but thankfully you don’t have to remember it, you can find it on the internet.
So now Maria deposits the Ethereum in Peter’s mailbox. She can have a peek inside and see the Ethereum there, in fact anyone who walks by can see that mailbox 2034 is filled with one Ethereum. This is part of the exciting part of Ethereum - that everyone can see all the transactions but without anyone having to share their identity. People can see there is one Ethereum in 2034, but no-one, except for Maria and Peter, will know it belongs to Peter.
Now let’s see how Peter gets his Ethereum - well he can see it’s there, so he doesn’t have to do anything. But if he wants to move it, he needs to open the box to send it to someone else. To open this he needs a key - and this is his own unique key, also called a private key, that he, and only he can use to open the mailbox. When he opens it he can remove the Ethereum and deposit into someone else’s box, let’s maybe say he is buying an online game from Microsoft, now he can deposit it into Microsoft’s box and once they can see the Ethereum received, they will ship the new game to him.
If Maria deposits into the wrong mailbox, she cannot move it back. This is similar to cash - once you paid it to someone you can’t easily get it back. Also note that no-one can move the Ethereum, except for Peter, who has the key to the mailbox. And if he loses his key? Well then no-one can access that post box, forever! It’s also important for Peter to make sure no-one steals his key, because if they do they can unlock his box and steal his Ethereum. So it’s important he keeps the key safe, or entrust it with someone that can do so.
Ethereum private keys give you access to the Ethereum system.