Vesting is the process by which individuals earn non-forfeitable rights to something, typically stock. This means that once you have worked at a company for a defined period of time, X, you will start to hold the value defined by the company in your offer. For example, imagine a company offered you 100 shares of stock as part of your compensation vesting over four years with a one-year cliff. This means that you will begin to accrue stock options after one year of employment (the vesting cliff), and that you will accrue an equal share of stocks over the remaining time, which is 25 shares for each year after the cliff.
Vesting selection at Investopedia
Rob Fitzpatrick's Equity basics: vesting, cliffs, acceleration, and exits at The Startup Toolkit
Andy Rachleff's What You Need to Know About Vesting Stock at Wealthfront