The piriformis is a difficult to reach muscle that runs from your sacrum to your (femur) thigh bone. When it begins to push against your sciatic nerve, often due to too much sitting, it can cause excruciating pain. When this happens, generally due to being inflamed ot tight is known as piriformis syndrome.
The piriformis work in conjunction with your Psoas (hip flexors) to help with both internal and external rotation of the hips, as well as to extend and flex. It rotates the thigh externally while extended (eg, during walking) and abducts the hip when the thigh is flexed at 90 degrees (eg, when crossing the ankle on the opposite knee while sitting). Although it's quite a small muscle in comparison to some others it's quite crucial to a healthy pelvis.
A tight piriformis can be from long periods of time with bad posture slouching in a chair, with your hips rotated outward places a lot of strain on your low back and makes your hips so tight that you create this tightness. Or can have been as a result of an injury.
In The Saddle
Humans are able to perform hip internal rotation on one side and the complete opposite on the other side. Often this can be more prominent once we are in the saddle. For example if you lack external rotation on one side, then your thigh may be sitting more into the saddle whilst then the lower leg is away, or you may find it swings and thus less effective. This will create a uneven balance on the horses back. Additionally this tightness or lack of even rotation means the pelvis cannot move freely as required.
Good hip rotation is vital to aid the rider stay balanced in the centre of the saddle.
The piriformis is one area that can be holding your riding back, it's one muscle of many in your core that are all involved in stability of the lower half of your body. The core works as a 'complete unit' all connected, there is so much to keeping your body stable, strong mobile and balanced
When you understanding the role that the muscles play you will be able to come more aware of areas that you may need to work on to bring more balance to your body and therefore your riding in the future.