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.
When a given country is able to acquire non-military means to persuade other potentially belligerent countries to want peace, such an act is referred to as the projection of soft power by the former. For example, one of the sources of soft power for the US is higher education. American universities have generally produced the most Nobel Prize winners in the fields of economics and the natural sciences. China, which desires to attain such achievements for itself, has thus channelled more resources into the development of domestic education, rather than on military build-ups. The Chinese government has also sent more Chinese students to American universities to study, contributing to a higher degree of complex interdependence between the two states. The Americans could thus be said to have been successful in attracting China into desiring what they want, in this case peace, through non-military means.