Proof-of-Work (PoW)

Is a consensus mechanism that ties mining capability to computational power. It is generally a piece of data which is difficult to produce but easy for others to verify and which satisfies certain requirements. In the case of blockchain, blocks must be hashed, which is in itself an easy computational process, but an additional variable is added to the hashing process to make it more difficult (a "nounce"). This process takes time and computational effort (by the "miner"). These two components provide a certain monetary value to the block and the miner is therefore rewarded. This is why a hashed block is considered proof of work. The main goal of a PoW system is to deter cyber-attacks such as a distributed denial-of-service attack (DDoS) which has the purpose of exhausting the resources of a computer system by sending multiple fake requests. 

Proof-of-Stake (PoS)

Proof-of-Stake consensus mechanism has the same overall process and goal as Proof-of-Work, the method to reach that goal is however entirely different. Miners are replaced by validators that lock some of their assets as a stake in the ecosystem. Following that, the creator of the next block is chosen via different combinations of random selection, based on the staked amount or the time the amount has been staked. When blocks gets added to the chain, validators get a block reward in proportion to their stake.

Proof-of-Authority (PoA)

Proof of Authority (PoA) is a modified form of Proof of Stake (PoS), where transactions and blocks are validated by approved accounts, also known as validators (these approved nodes must pass a preliminary authentication). Instead of using a stake with monetary value, the validator's identity performs the role of stake. The process is automated and does not require validators to constantly monitor their computers, the node must however be kept uncompromised. PoA is suited for both private networks and public networks, where trust is distributed. The chain has to be signed off by the majority of authorities, in which case it becomes a part of the permanent record. This makes it easier to maintain a private chain and keep the block issuers accountable.