A web wallet is a wallet that works like an account on any other website. It lets you login on any device using a username and password.
MyEtherWallet
MyEtherWallet is probably the most popular Ethereum web wallet.
Web wallets, however, are not secure at all and should really not be used at all. Recently there was an issue with MyEtherWallet where the hackers were able to track the accounts of users that were on the site at the time of the hack. The amount of ether and ERC20 tokens the attackers were able to steal is unknown.
It’s also possible to get phished where you give a fake website your login credentials which they use to login on the real MyEtherWallet to steal your funds.
If you do decide to use MyEtherWallet, definitely use it with a hardware wallet and not as a web wallet.
MyCrypto
MyCrypto is a fork of the MyEtherWallet code when the founders of MyEtherWallet had a disagreement.
Like MyEtherWallet, MyCrypto is a web wallet and is therefore not very secure. However, you can pair MyCrypto with a hardware wallet like a Ledger or Trezor so that your private keys are not held on a server you do not control.
If you do it this way, MyCrypto acts as a sort of wallet interface for you hardware wallet.