Acupuncture can usually have some effect on all types of headaches, including migraines. I find tension type headaches respond the best to acupuncture but it usually depends on the individual, how long they have had the headache for, history of headaches etc etc.
Acupuncture stimulates the release of adenosine which is a neurotransmitter. It is an inhibitory neurotransmitter which means it can depress the CNS and promote sleep (often why people feel sleepy during and after a treatment) which is one of the ways acupuncture can help tension type/stress induced headaches. Adenosine also plays a role in stimulating the release of endogenous opioids (the body's natural painkillers).
I hope that gives you a little more insight! :)