Block validation implies that a set of transactions are bundled together using a process or algorithm and attached to the blockchain. One of those algorithms is called Proof of Stake, and it permits stake delegation using dedicated nodes named Stake Pools.
Proof of Work (PoW)
The most popular consensus algorithm is called Proof of Work (PoW) and is used by Bitcoin and some of the coins developed using its codebase: Litecoin, Bitcoin Cash, Bitcoin SV, Monero, etc.
The blockchain is a public and distributed ledger containing all the transactions packed inside blocks. Each user is only allowed to spend his coins once. Only verified blocks can be added to the blockchain. Since the ledger is public any attempt to tamper with the blockchain will be rejected by all the network participants.
Tamper detection is performed hashing block data. Hash functions are very easy to perform but are really hard to reverse. The possibility of reconstructing the data from its hash is negligible. If someone alters the blockchain, a cascade effect will take place since the has of any block depends on the hash of the previous blocks. Perform a hash is very easy. This is why the network uses the concept of difficulty. The miner performing the hash must achieve some degree of challenge, for example performing a set of hashes with some condition. PoW consumes lots of energy and CPU power considering the aggregated work of all miners. The challenge is tuned so a block is mined every 10 minutes. In the same action of validating transactions, some new-minted coins are rewarded to the miner. The rewards assigned to miners halve every few years. This process is called Halving.
Proof of Stake (PoS)
PoS is an alternative, and probably a better way to validate transactions. Instead of miners, PoS uses validators. The Pos algorithm used by Cardano is called Ouroboros. These are the nodes, named stake pools, in charge of validating and creating new blocks. Each network participant can stake his coins in the stake pool. Proportionally to each node stake, there's a probability to be selected as a block validator. A lottery takes place every day and the stake pools responsible for validating the transactions are selected. Stake pool selection must be truly random for the algorithm to be secure. Ouroboros implements multipart a coin-flipping protocol. If the stake pool succeeds in validating the block, it receives a reward that is distributed proportionally between all the people that contributed to the node stake. Each stake pool can keep for himself a percentage of the rewards to cover the costs of running the node.
What is delegation?
Each holder of coins can delegate some amount to any stake pool. Delegation does not mean the transfer of funds. The coins just remain locked inside the node until his owner decides to delegate to another stake pool.
Users can delegate their stake using their wallets. For example the Yoroi wallet:
Currently, Ouroboros is being tested in the Cardano blockchain. They provide a calculator to estimate the rewards according to the amount staked. The people behind Ethereum is working to hard fork their blockchain and use the PoS protocol.
You can read more about Ouroboros here.
More about Ethereum Migrating to Proof-of-Stake.
More about stake pools and the Cardano delegation process.