In short, angular velocity is a radius-independant way of representing the turning speed. Suppose you have a plank of wood, with a hole in the middle, and you are spinning at a constant speed: The closer you are to the centre the slower you are moving. If you are at the very edge it is moving fastest, if you are standing right at the centre then you are just spinning aound on the spot.
So the speed with which you move is dependant on the speed with which your plank spins, but also the distance from the centre.
This is where angular-velocity comes in: Angular veolcity is simply the speed of rotation (as an angle), divided by time. Hence the units are: radians s-1, or "radians per second".
Now that you have your angular velocity, it is a simple matter of multiplying your distance from the centre (the radius) by the angular velocity, and you will have your actual speed.
This simple calculation is possible becuase of the magical powers of radians... a radian is the angle at which the arc subtended is equal to the radius of the sector. So if youre doing 1 radian/sec and your radius is 1m then the arc travelled is 1m per second.