In the field of International Relations, power is often defined as the ability of one country (Country A) to get other countries to do what Country A wants (or to refrain from doing things that Country A does not want done). One way to accomplish this is through "hard power." Hard power is usually defined as the use of military and economic might to gain power -- to make a country do something by threat of military or economic force.
Soft power, by contrast, is the power of Country A to get other countries to want to do what Country A wants. If Country A can persuade other countries to do what it wants on their own, that is soft power. So soft power is more of persuasion. It is the ability to get other countries to have the same goals that you do so that they will want to do what you want them to do.