First aid

Essentially, the heart is a pump whose purpose is to keep the blood circulating. The muscles of the heart expand and contract, pushing the blood out of the heart and drawing in new blood. When a person loses consciousness their heart may stop beating and the blood won't circulate, and this can cause great damage in areas like the brain. By pressing down on the chest in a rhythm you are forcing the heart muscles to contract and expand, and therefore to keep the blood circulating. In some cases (e.g. someone who was drowning) this forced activity of the heart can make the heart muscles start working again. I guess it is something similar to priming a pump in order to make it work

When you perform CPR, you are essentially breathing for the person.  CPR is usually just something that is used to keep a person alive until professional medical help arrives.  By breathing into the mouth, you are making sure that the person is receiving air to the brain, and by pressing on their chest, you are helping their heart to beat.  CPR will usually not save one's life.

 -Anya

Chest compressions (part of CPR) are intended to keep the blood moving around the body. Mouth to mouth is intended to keep air going into the lungs.

If someones heart has stopped beating in a cardiac arrest then it's rare that a thump on the chest or chest compressions will make it start again. They mostly need treated with an electric shock defibrillator device.

The chest compressions that you do in first aid are really just buying time until a defibrillator arrives - and this is why you should never stop until professional help turns up on the scene.