What does the 'deterministic' mean in this context? What would be a non-deterministic wallet?
Seed could be a sequence of words (this thing needs to be backed up and stored safe!)
Huge advantage is that you can save the seed in safety deposit box in a bank, written on paper - totally non electronic way.
Then you can recreate wallet from seed at any time and manage your funds.
If your bitcoin private key only exists on a piece of paper and not on any networked computers, then there's no way that malware or a company being hacked or an exchange going down is going to affect its balance.