Yes, they can be brought on by stress. I get them if I drink too much caffeine too. BUT they can also be caused by a heart condition like atrial fibrillation which should get checked out at some stage (ie. it is not an emergency as long as you're not feeling unwell or have chest pain or shortness of breath).
I think palpitations is when your heart is exerting extra force so that you can feel it, which isn't too dangerous as long as you're healthy and it doesn't last more than a few minutes.
Or in atrial fibrillation, it is when the atria of the heart are contracting very fast and not coordinating with the ventra. This can be dangerous if it is prolonged and left untreated because it means your circulation isn't at its best. If you feel your pulse while you have palpitations and it is fast and erratic, you should get checked out.
Hope whatever is causing you the stress works out!