I recently bought my first bitcoins although I've known about them for a few years. I have an online wallet but I was wondering how the offline one worked? I know that once you have bitcoins in it and lose it due to computer failure, they're gone. Could I for example make multiple copies of my wallet and upload them to online storages? If so, lets say that I put more bitcoins in the original wallet at a later time, will the other copies update to the number of bitcoins I added to the original wallet after they're connected to the internet?
Bitcoins are not stored in your wallet. Bitcoin transactions are stored in the globally distributed ledger called the blockchain (not to be confused with the website blockchain.info). When someone sends you bitcoins he signs off ownership of the coins to your address. That transaction is recorded in the blockchain. For you to be able to then spend those coins you need the private key behind your address and that is what is stored in your wallet. A wallet is basically a collection of private keys and a private key is basically a really, really large number.
To receive coins you don't have to be connected to the internet. To spend coins you do.
An offline wallet is wallet that is installed on a computer that is kept offline. It is considered safer than a wallet on an online computer.
Unless you have a large amount of coins I suggest starting by using a desktop client like electrum. Definitely move away from a blockchain.info mywallet. Don't worry about offline wallets for now. You can look into them later when you understand bitcoin better.
As far as backups go with electrum it is very easy to do. You just write down your 12 word "seed" on a piece of paper. The seed is like a master key and all your addresses, past and future, are derived from that. And yes your balance will update if you restore from seed in future.
