Validators are responsible for committing new blocks in the blockchain. These validators participate in the consensus protocol by broadcasting votes which contain cryptographic signatures signed by each validator's public key.
Some Proof-of-Stake consensus algorithms aim to create a "completely" decentralized system where all stakeholders (even those who are not always available online) participate in the committing of blocks. Tendermint has a different approach to block creation. Validators are expected to be online, and the set of validators is permissioned/curated by some external process. Proof-of-stake is not required, but can be implemented on top of Tendermint consensus. That is, validators may be required to post collateral on-chain, off-chain, or may not be required to post any collateral at all.
Validators have a cryptographic key-pair and an associated amount of "voting power". Voting power need not be the same.
There are two ways to become validator.
+2/3 is short for "more than 2/3"
A block is committed when +2/3 of the validator set sign precommit votes for that block at the same round. The +2/3 set of precommit votes is called a commit. While any +2/3 set of precommits for the same block at the same height&round can serve as validation, the canonical commit is included in the next block (see LastCommit.