A recent question centered on the fact that higher and higher rep counts for an exercise (e.g. pushups) stop building strength, but 'build stamina.' Do they in fact build any sort of muscle-specific stamina, or is it all stamina just the same cardiovascular training?
There are more explanations than this one, but one is what type of muscle fibre you strengthen. Muscle fibre type 1 are slow, weak but have high stamina, type 2 have low stamina but are stronger and faster.
This is why some people are born to be sprinters while some are born to run long distances.
If you do many reps, your type 2 fibres will tire and the type 1 fibres will do most of the work, meaning they will be strengthened.
This is also why doing 10-12 reps is ideal for volume, it will strengthen both fibre types.