In Chapter 2 of Reference , one of the footnotes has a definition of a radian. For a unit circle with a radius of one unit of length called $ u$, one radian is the angle corresponding to an arc-length of $ u$. In degrees, one radian is approximately 57 degrees, which is perhaps easier to visualize. A diagram of one radian is included here for reference.
References Konrad Knopp. Theory and Application of Infinite Series. Dover Publications. 1990.