Velocity is a measure of the amount of work a Team can tackle during a single Sprint and is the key metric in Scrum.
Velocity is calculated at the end of the Sprint by totaling the Points for all fully completed User Stories.
Velocity is a key feedback mechanism for the Team.
It helps them measure whether process changes they make are improving their productivity or hurting it.
While a Team's velocity will oscillate from Sprint to Sprint, over time, a well-functioning Scrum Team's velocity should steadily trend upward by roughly 10% each Sprint.
It also facilitates very accurate forecasting of how many stories a Team can do in a Sprint. (In Scrum this is called using Yesterday’s Weather.)
For forecasting purposes the average of the last three Sprint's Velocity should be used.
Of course, this means it takes three Sprints of experience for a Team to determine its Velocity accurately, which can sometimes be difficult to explain to impatient stakeholders.
Without Velocity, Release Planning is impossible.
By knowing Velocity, a Product Owner can figure out how many Sprints it will take the Team to achieve a desired level of functionality that can then be shipped. Depending on the length of the Sprint, the Product owner can fix a date for the release.