"External" means the bearings are outside of the bottom bracket shell. The crank spindle is hollow and lighter than the solid spindle of a square taper BB.

The bearings are spaced farther apart which supports the spindle better.

Theoretically there is an advantage but in the real world, I don't think so. I have every kind of bottom bracket.

Chris King makes high quality external BBs. They are expensive.

Many people say square taper BBs are more durable than external BBs.

I just replaced the BB on my fixie with a Interloc Racing square taper BB. It's as sweet as anything I've ever used.