Radians are an absolute measurement of an angle,degrees are not. If you try and use degrees for certain kinds of problems,they will not work because they are an abitrary way of measuring.
One radian is defined as the angle subtended by an arc length on a circle,where that arc length is the same length as the radius of the circle- that's where the name radian comes from.
Put more simply - draw an arc on a circle where that arc length is the same as the length of the radius. Join the ends of the arc to the centre of the circle to make an angle. That angle is one radian.
