Staking is the process of putting reserve assets on the line in order to participate in a Proof-of-Stake cryptonetwork’s consensus mechanism.
Typically, users lock up assets in a wallet, out of their reach for some amount of time. During staking they become validators on a network and are rewarded for their participation. Staker/validators in Proof-of-Stake environments are the equivalent to miners in a Proof-of-Work environment.
The reasoning behind staking is to promote honest activity. Actors that lock up value (put skin in the game) are incentive to act honestly because if they are found acting dishonestly their stake is removed, and nobody who commits their value would want to lose their investment.