Typically what is meant by an online wallet service is that the service handles the key and address management for you. You typically don't have to worry about creating new addresses or backing up your private keys. However, an online wallet has the downside that if it gets hacked, there is a chance that an attacked could steal all of your Bitcoin because that attacked would have access to your private key. Some online wallets, like Coinbase claim to have 90% of the funds in cold storage. Cold storage typically means that the coins are sent to addresses that haven't been used AND were generated on a non-networked computer. These keys then are printed to paper and saved to USB drive and then put in a physical security box in a place like a bank.