The radian is known as an SI derived unit, and the degree is an SI accepted unit of angle. The degree is defined as 1/360th of a circle. The definition of a raidan is more complex, and an explanation follows, but it is often enough to know what there are 2*pi radians in a circle.
A radian can be measured by taking the radius of a circle and measuring the angle created when the length of that radius is wrapped around the circumference of the circle. There are useful diagrams and further explanation at the Wikipedia page on Radians