Vesting means that you will receive your equity over time.
Vesting schedules are commonly attached to securities like options or restricted stock and provide an incentive for employees to remain at a company.
Vesting has two components: Duration and a Cliff.
A vesting duration is how long and how often you will receive your shares. The most common vesting duration is monthly over 4 years, which means that you will receive 1/48 of your equity each month over the next 4 years.
A cliff sets the minimum amount of time you need to work at a company to receive equity. The most common cliff is a 1 year cliff (with 4 year vesting). That means that although your shares will vest monthly over 4 years, you won't receive any until you complete 1 year of service. At the 1 year mark, you'll receive 25% of your equity.