What is Proof of Stake?
Proof of Stake is the name given to set of algorithms that endeavor to solve the blockchain consensus problem by restricting the forging of new blocks to nodes that have a vested interest, or stake, in the continued success of the cryptocurrency. In contrast, Bitcoin uses a Proof of Work algorithm in which nodes are required to perform a computationally very expensive task to mine a new block. The trouble with Proof of Work is that as the difficulty of mining new blocks increases, the generation of these blocks becomes limited to a few, centralized pools that have the infrastructure to perform these tasks.
Cardano's Proof of Stake algorithm, Ouroboros, is a peer-reviewed and provably secure system that keeps the cryptocurrency network decentralized because the security of the blockchain does not depend on being able to solve an ever-increasingly complex computational task.
Stake pools, like Arcadia's ADAMS & TESLA, are the nodes which can participate in the Proof of Stake consensus mechanism to create new blocks for Cardano. For a pool to win positions as a slot leader, the pool operator and delegators must use their combined staking power to demonstrate to the network that they are acting in good faith. Without enough combined stake, the pool will not be elected to produce blocks. This discourages attacks because a significant investment must be made in the cryptocurrency before there is an opportunity to harm the blockchain.
Below are two videos that explain the Ouroboros protocol. The first video (8 minutes) is a brief explanation of what Ouroboros does that serves a good introduction. The second video (60 minutes) is a more in-depth explanation of how Ouroboros works.
Watch Video 1
Watch Video 2