MyEtherWallet in generating a wallet for you generates the public and private keys (which are really the only two pieces you need), and then provides several backups for you. As I mention in my beginner's guide to Ethereum:
- Password: what you created in the first step
- Keystore File: a file you downloaded, which starts with UTC--.
- Private Key: A 64-character hexadecimal string.
- Paper Wallet: physical piece of paper you printed off your computer. It has your Private Key written on it.
- Account Address: a 40-character hexadecimal string.
These five things are redundant backups of each other. They're
designed such that if you lose access to one, you can still get at
your funds. Here's how they work together: your private key (#3) is
the only thing you need to access your funds. That makes it both very
convenient and very dangerous (if an attacker gets it, they have your
funds). And, the private key doesn't have any protection of its own,
so it's up to you to use outside means to keep it safe. The paper
wallet (#4) is a useful way to store your private key in a physical
form. The paper wallet has both private key (#3) and account address
(#5) on it, both written out as a hexadecimal string, and as a QR code
(which makes it easy to input into a mobile device that has a camera).
It's intended for you to fold the right side of the paper over and
tape it, so that the private key values are hidden and sealed away
(helps prevent accidentally showing your private key to a security
camera as you're walking around with your paper wallet). The keystore
file (#2) and Password (#1) work together. Either of them individually
is useless for getting at your funds; the keystore file (#2) has the
private key (#3) encrypted inside it with the password (#1). So, an
attacker would need to get their hands on both to steal your funds.
So, separate those two into two separate locations, so an attacker
would have to hack two different things in order to get them both. The
account address (#5) is the least essential but most commonly used
part of your wallet. The account address (#5) can be derived from the
private key (#3), so as long as you have the private key (either the
paper wallet (#4), or the keystore file (#2) and password (#1)
together), you can re-calculate the account address.