The first 20% of the stance phase - from landing to toes-off - relies predominantly on our quadriceps and gluteus muscles. They prevent the knee and hip from collapsing when the knee bends. The two muscle groups help us to maintain balance and not fall forward/laterally.
During the midstance, gluteus muscles remain active, while stability also comes from more passive structures, like the hip capsule and various ligaments. The hip extension sees the hamstrings kicking in, too.
Given how active the gluteus medius is to help with overall balance, many studies hypothesized its weakness may contribute to running-related injuries.
People with patellofemoral pain syndrome seem to have reduced gluteus medius strength, which results in a hip drop at foot impact. The exact mechanisms on how this impacts hip and knee biomechanics remain unclear.
To sum it up, if you want to improve your running performance and try to stay injury-free, training your gluteus muscles - the gluteus medius in particular - is never a bad idea.