Staking is like earning interest on the coins you hold. In POS it supports the network.
This is a nice concise answer.
Staking is the reward you receive for supporting the network by holding coins and running a node. If you have coins in a wallet that is a POS coin your supply of coins will grow as long as you are holding the coins.
Staking is also related to time. You are paid an amount based on an amount of time that has elapsed. Some coins also have limitations on when the coins will stake and for how long.
Different coins have different values for how the staking works and these values are important for assessing the value (or future value) of a coin.