Sometimes to treat foot problems you need to change the posture or alignment of the foot. The arch may need supporting or the heel may need to be tilted inwards or outwards. At times there are conditions in which the foot needs to be tilted in some more and laterally wedge insoles are used for that. Two of the more common reasons for doing this include peroneal tendonitis and medial knee osteoarthritis.
This is an overuse injury of the peroneal tendons on the outside of the ankle and foot. The pain is typically just below and/or just above the outside ankle bone (lateral malleolus) and is made worse with increased activity. The lateral wedge in the shoes decreases the activity of the peroneal muscles, so these is less force on the tendons. For more, see this article on peroneal tendonitis.
Medial Knee Osteoarthritis
This is the wear and tear osteoarthritis that occurs in the medial or inside compartment in the knee. A number of lab based studies have shown that a lateral wedge under the foot is effective as reducing forces in that compartment and reducing the symptoms of medial knee osteoarthritis. It is thought that it could help by changing the weightbearing angle that goes through the lower limb. The clinical trials on the use of lateral wedging for medial knee osteoarthritis have not shown good results, with most studies showing that it helps some and does not help others, so some experimentation may be needed to see if it can help. For more, see this thread on lateral wedging for medial knee osteoarthritis.