When you receive some kind of gift, be it money or property, through a will, that gift is known as a bequest. Your aunt left you a bequest of the earrings she always thought you admired.
The noun bequest is something one arranges to give away after death, sort of a gift from beyond the grave. Basically, putting a bequest in a will is a way of making sure the right person will get certain goods after your death. If you are very wealthy, universities and charitable organizations may court you in an attempt to gain bequests for their institutions.