Shin rotation is rotation of the shins relative to the thigh bone.
With respect to the knee, shin rotation can only happen when the knee is bent.
External rotation of the shin relative to the thigh is driven by the gluteus maximus, tensor fascae latae and biceps femoris (both heads). It also may be driven by the vastus lateralis of the quadriceps.
Tensor fascae latae and some fibers of the gluteus maximus both attach to the Iliotibal tract (or IT band) which runs down the side of the thigh to attach to the top of the outer edge of the tibia, just below the knee and just in front of the fibula. With the knee bent, tension from these muscles acting via the IT band can pull back on the outer edge of the tibia causing external rotation (or resisting internal rotation) of the lower leg. If the vastus lateralis attaches to the IT band then it too can help drive external rotation of the lower leg relative to the thigh.
The biceps femoris long head attaches from the sitting bone to the top of the fibula. The short head of this muscle attaches from the back of the thigh bone to the top of the fibula. The short head can activate if the thigh is stable while the long head can activate if the pelvis is stable. The amount of bend in the hip may also affect which of these muscles is activates to help cause shin rotation.
Internal rotation is driven by the semitendinosus, sartorius and gracilis, all of which attach to the inner edge of the tibia just below where it flairs outwards to help form the bottom of the knee. Internal rotation may also be driven by the semimembranosus muscle.
Semitendinosus and semimembranosus both originate from the sitting bone, just like the long head of the biceps femoris. Gracilis originates near the pubic bone and sartorius from the ASIC, the point of the hip.
The different origins of these muscles may allow internal rotation to be created in a variety of leg positions. It also means that external rotation can be resisted in a variety of leg positions. If the lower leg is stable, then these muscles can help stabilize the pelvis.
Pelvic/lower leg stabilization may result from these muscles working against each other.
While these muscles can cause rotation of the shin relative to the thigh when the knee is bent, they can help rotate the shin and thigh together when the knee is straight. And if the lower leg is fixed, then can help stabilize the pelvis.
With the foot and shin stabilized against rotation and bearing weight, these muscles can all be used to help stabilize the pelvis. They could also be used to help control (and create) rotation of the pelvis relative to the leg.
With the foot lifted (and not bearing weight), these muscles can be used to rotate the shin if the knee is bent. They can also be used to stabilize the knee and help to support the weight of the leg if the knee is straight.
Because some of the external rotators attach to the fibula (the biceps femoris), fibula stability can be important, particularly when the feet are bearing weight but also when stretching the muscles of the leg or working at extreme (close to end range) positions.
Muscles that work on the fibula from below include the soleus (the deeper of the two calf muscles) and some intrinsic muscles that help to shape the feet.
With respect to the feet, (and with the feet on the floor) shin rotation generally causes a change in shape of the inner arch of the foot. Rolling the shins outwards tends to accentuate the arch while rolling them inwards tends to flatten it.
This is driven by muscles that attach from the bones of the lower leg and cross the ankle to attach to the bones of the feet.
You could roll the shins externally and lift both the center of the inner arch and the inner forefoot. Or you could roll the shins externally while keeping the inner forefoot grounded. You may find in the latter case, the inner forefoot, while staying in contact with the floor, is pulled back towards the heel resulting in a pinching or grabbing action between the inner forefoot and heel.
Rolling the shins internally, you could work at keeping the outer edge of the foot on the floor or you could allow it to lift.
The ankle and heel bones are stacked more or less on top of each other (talus on top, calcaneus below) .
Rolling the shins externally (with the feet on the floor) tends to stack the ankle and heel bones while rolling the shins internally tends to collapse them.
Along with the flattening of the inner arch that accompanies inward rotation of the shins relative to the feet, the collapsed position may allow the knees to go further forwards while keeping the heels flat on the floor.
Note that though I use the term collapsed, this position isn't necessarily a bad one. You could think of it as a relaxed foot position. That being said, it is possible to stabilize both "heel bones" and the shin bones in this position. Relaxed in this case means that it's the position the bones assume when succumbing to gravity without any muscular resistance. Muscle activity could be used to stabilize or even muscle the bones of the foot into this position.
In chair pose, with hips above the height of the knees or at the same height (or lower), you could roll the shins in or out without causing the knees to move inwards or outwards. The inner arch and heel will collapse with the inwards rotation and lift and become stacked with external rotation.
You could use foot actions to cause the knees to move inwards or outwards. In this case the actions of the foot (say shaping the arch and stacking the heel and ankle or collapsing the arch and heel and ankle).
Keeping the foot relative stable, you could rotation the shin inwards or outwards using the shin rotators. In a squat you may find that this adds tension to the inner thighs with inwards rotation and to the outer thighs with external rotation.
In a pose like warrior 1 and focusing on the front knee, you could keep the foot stable, and rotate the shin outwards or inwards. If you work at keeping the knee and pelvis stable you'll add tension to the inner or outer thigh as for squat, or you may find you can use external rotation to either move the knee inwards or the pelvis outwards and vice versa with internal rotation.
Keeping the pelvis and thigh stable, you can use external rotation of the shin to lift the inner arch and stack the heel and ankle bone. You can use internal rotation of the shin to collapse the arch, ankle and heel.
The external shin rotators can include the biceps femoris which attaches to the top of the fibula and portions of the gluteus maximus and the whole of the tensor fascia latae which via the iliotibial tract attach to the top of the tiba, just in front of the fibula. The internal shin rotators can include the sartorius, gracilis and semitendinosus, all of which attach to the top of the inner surface of the tibia just below the bulge of the knee.