Poison oak is a member of the Anacardiaceae - the Cashew Family. The family has many members that cause skin irritations, including (for many people) the cashew plant itself and the mango. In all cases the irritant is an oil that is borne in the outer conducting tissue of the plant - its phloem. Phloem as a tissue is composed of several cell types. One of these is a secretaory cell that generates the irritating substance, which is then carried within the surficial layers of the plant in laticifers, anastomosing canals. When one breaks the skin one releases the irritating chemical.

The active substance is Urushiol. Here I refer you to the excellent summation at Wikipedia.

What does it have to do with Chemistry? Well, on the one hand, the plant is synthesizing urushiol (a chemical) from hydrogen, oxygen and water (see the complex diagrams at Wikipedia) so it is acting as a natural chemist. Further, it is by the study of its composition that human chemists can understand the composition of urushiol and potentially suggest ways to reduce its irritating properties. Finally, it is by biochemistry that we can understand how urushiol creates the irritation that it does in many, but not all, humans.

Yes, this can be a burning question, so to speak.Poison oak contains an oil called urushiol. Urushiol triggers a reaction from your immune system called an inflammatory response. Your immune system protects you from germs and parasites. But some things that are not germs or parasites can also trigger a response from the immune system. That's what an allergy is, a big immune system response to something that would be harmless otherwise.

Chemistry is important because the shapes of molecules make them more or less likely to trigger an immune response. Antibodies have particular shapes that bind with other molecules. Some shapes are more likely to fit antibodies than others are. You could develop an allergy to almost anything, but some things are particularly likely to cause an allergy. You may know a few people who are at least a little allergic to peanuts or cats. You probably don't know anyone allergic to apples or glass. About 90% of people will have an inflammation reaction to the urushiol in poison oak.

Why do you think some plants make urushiol? How would it benefit the plant

Poison oak contains a chemical called urushiol that is produced in the leaves, branches, roots and flowers of poison oak (scientific name Toxicodendron diversiloba). The rash is caused due to the bodys immune system trying to fight the poisonous oil. The oils can be transferred directly from the plant or can be present on your clothes, your dog, etc and then transfer to you.

The chemical urushiol is what causes the irritation from poison oak, poison ivy and sumac. It is found in their leaves, stems and roots and has this chemical structure:

and the group that says "R" can be any one of the following:

The chemical (usually a mixture of several above) penetrates and binds to your skin cells. The long carbon chains of the R groups cause the chemical to bind very tightly making it difficult to wash off. Once the compound is bound to your skin cells your body sees those cells as dangerous causing an immune response. The itching redness and rash is the result of your body trying to destroy the cells the urushiol is bound to.