Upgrades points are earned by earning cash. The way you earn cash is by shrinking balls. Since higher level balls earn more cash, you can earn more upgrade points with higher levels.
Pending points are shown to the right as well as the coins required to earn the next point
Upgrade points can be redeemed by doing a prestige.
With upgrade points, you can spend them on upgrade options, the crown located on the bottom right. If you unlock a tower, you'll have to close the upgrade panel and re-open it for that option to be present.
If you would like to start over with all your upgrade points, you can do a "Respec", the bottom option in the prestige menu.