Hill repeats turbocharge the number and size of mitochondria in your muscle fibres, significantly increasing their output of aerobic energy.
They improve your ability to generate force fast. When running the prime directive each time your foot lands during a stride is to generate enough force to get back into the air. The faster you do that, the quicker you start your next stride.
Generating force needed to do this is a a two-step process. The first part of the process is you accelerate your foot downward, creating force when your foot strikes with the ground.
The second part of the process is that your muscles generate additional force while your foot is on the ground.
Hill repeats will shorten the distance your foot travels downward (lessening collision force) and require extra overall force generation to fight gravity, improving your ability to produce muscular force on the ground.
Overtime this should result is a quicker cadence (i.e., more steps per minute) and increased stride length. Put them both together and it means you should get faster!
Hill repeats also:
significantly strengthen all muscle-fibre types.
rewire your nervous system to recruit all fibre types simultaneously.
increase your heart’s stroke volume.