You've likely known that with mouth to mouth rescusitation, you breathe into the other person's mouth to try to get air into their lungs and oxygen to their tissues. So, what gas do you breathe out? Carbon dioxide right? So how can you get Oxygen into the person's mouth simply by breathing into it?
As it turns out, when you breathe out, you expel a large amount of oxygen. Your body only uses a small portion of the Oxygen that it inhales. The rest is breathed out (or remains in dead spaces where a small amount of gas inhaled doesn't get involved in gas exchange). Why is this? For one, your tissues do not always require a high oxygen content. You require more oxygen when exercising, and it's a nice security blanket to be able to retrieve more stored oxygen from the blood. However, you never use all of the oxygen that you breathe in. In fact, most of it doesn't get used by the tissues.
Thus, when you do mouth to mouth, you are breathing out enough oxygen into the person's mouth to try to oxygenate their tissues.