In contrast to just holding coins in your wallet or locking them in a smart contract (masternodes), some tokens added randomness to the process of staking and voting so that bad players have a hard time manipulating outcomes. The process is similar to a lottery in which the number of crypto coins you hold is equivalent to holding a given number of lottery tickets. Staking systems can also allow delegation in which each individual delegates their voting rights and earned income to a trusted party. Those delegates then earn all the rewards for block validation and pay their loyal supporters some form of dividends in return for their vote.
All blockchains have one thing in common: transactions need to get validated. Bitcoin for example does this in a process called mining which is known to use a lot of electricity (Proof-of-Work). But there are also other forms of validation often referred to as the consensus mechanism. Proof-of-Stake (PoS) is one such consensus mechanism that can come in different variations and hybrid models. For simplicity reasons, we will just refer to all of these as staking. Coin staking gives currency holders some decision power on the network. By staking coins and tokens, you gain the ability to vote and generate an income. This is quite similar to how someone would receive interest for holding money in a bank account or giving it to the bank to invest.