If you look at an airport diagram, (they can easily be found online), you'll see some taxiways that are at a 90 degree angle to the runway. An aircraft would have trouble making a turn onto one of those unless it was moving slowly. Other taxiways are at an angle to the runway--aircraft don't have to slow down nearly as much to exit on those taxiways, thus "high speed".
The less time each aircraft spends on the runway, the more traffic an airport can handle.
I thought I remember a reference saying that high speed taxiways were a 50 or 60 degree angle to the forward facing runway in use.. I know it's mentioned somewhere, but not quite sure.
Also in contrast, you may hear ATC asking to use the 'reverse' or 'reverse high speed, which is a high speed intersection, but for the opposite runway; for example, landing on 24R at KLAX, and the aircraft exits on taxiway Y, which is actually a high speed for 6L.
BL.