Well, flying on a given radial lets you approach the beacon from the specified heading. Useful when you want to get to an airfield and arrive matching the rwy heading.
Today, some squad members and I used it for taking off in crappy weather: we took off at 30 s intervals, then turned and followed a certain radial away from the field. Since we were all on the same radial, we were guaranteed ending up on a line later when we broke the clouds. If you know your current radial and the distance, you can essentially fly in a trail formation even though you can't see eachother, say leader is at radial X 10 km out, 2 is at radial X 8 km out etc.
There lots of cool tricks you can do with your approaches too, check the pics on p. 115 and on in the manual.
Also, your current radial plus the distance to the beacon form a polar coordinate system in the plane, so you can easily relay your position to others. Think Bullseye.