Cardano is a Proof-of-Stake network. This is different to a Proof-of-Work network like Bitcoin. In Bitcoin you use computer power to secure the network, but in Cardano you stake coins to secure the network.
Staking has not started yet. It is expected to start March next year.
You will not need to leave your computer on. You will be able to delegate your stake from your wallet to a stake pool, then you will receive rewards when the pool makes a block. The pool will not be able to lose your coins, as you only delegate them, you don’t give them.
Does it make sense?