As the name suggest a web wallet lets you interact with your wallet on the blockchain via a web browser or extension. There are two types of web or online wallets. Hosted vs non-hosted wallets.
Hosted wallets keeps your private and public keys stored on their servers (with some exceptions). Examples of hosted wallets are exchange wallets (Binance, Coinbase, OKEx, etc) or dedicated Bitcoin and cryptocurrency wallets (Blockchain, Freewallet).
They offer different protection in the case of lost keys, email, etc. Non-hosted wallets are where your private keys are not stored on their servers. And instead you are responsible for storing your private keys. One of the most popular non-hosted wallets is MyEtherwallet (MEW).