In a proof of work system, miners compete to solve a computationally difficult puzzle in order to create a new block and earn a reward. This process consumes a lot of energy and resources.
In contrast, in a proof of stake system, like what Cardano uses, the creator of a new block is chosen in a deterministic way, depending on the stake (how many coins they have) are in a given stake pool. This means that the more coins a stake pool holds, the more likely that pool is to be chosen to create a new block.
Once a stake pool has created a new block, the pool receives a reward at the end of the epoch and those rewards are then distributed proportionately, based on the amount staked, to the pools stakers.
This process is typically more energy efficient than proof of work, because it does not require solving computationally difficult puzzles.