A bevel is any edge of a structure that is less than or more than 90 degrees. Bevel cuts are cuts designed to create this sort of angle on the edge of a structure. They have a number of uses in carpentry, crafting and welding.
Bevels are often used in carpentry to create pieces that are more aesthetically pleasing, more resistant to weathering, or simply to soften an edge so as to not cause injury. For example, a piece of wood meant to serve as trim around the base of a wall may be beveled to prevent injury and give a decorative appearance.
Bevel cuts are also a technique used in carpentry for hiding a joint by fastening together two pieces with edges that make complementary angles. The pieces are slightly overlapped and appear to be a single piece of wood if joined together correctly.
Bevel cuts are also quite strong and are used in welding, where the beveling technique is used to provide added support to heavy loads brought to bear on the joint.