Staking is the process of locking up a digital asset ($ATOM) to provide economic security for a public blockchain. You can learn more about staking $ATOM in the official documentation.
Staking ATOM tokens is relatively straight forward, after you stake your tokens are immediately earning rewards. Periodically you'll be able to claim these rewards, which are not automatically added to your staked balance, so you'll need to restake these rewards for compounding earnings.
When unstaking there is a 21 day lockup period, after which you can withdraw your ATOM.