First of all the angular space is usually represented by the Greek omega (big o) "ω" and not "w", unlike a lot of students (and teachers) think. But that completely aside.
Radian is not a unit like meters or seconds. It's a way to denote that the result is a sort of normalized answer for the angle that is being passed per second.
It means that it is the distance that is being passed per second if it would be on a circle with a radius of 1 meter. The whole circle is 2Pi in that case.
You could also use percentages (divide by 2PI and multiply by 100%) or degrees (divide by 2Pi and multiply by 360°). But those are rarely used.
Weird... I just finished this chapter in math. Anyways radians are usually meased in comparison to Pi... 2pi = 360 degrees... ok well I cant really explain it without really knowing the question.
I remember my Calculus professor actually explained the other day why Pi is equal to 180 degrees. It was very interesting, yet utterly useless, hence the reason I forgot it mere minutes later.
"w" is angular velocity in physics, w=v/r = (distance travelled around the circle)/(time)/(radius of the cirtle) =(distance travelled around the circle)/(radius of the cirtle)/(time), since (distance around the circle)/(radius of the circle) is the definition for "radian", so the unit for "w" is just "radian/second".
But we often omit the unit "radian".