Soft power is the ability to obtain what one wants through co-option

Co-option

A co-opting or less frequently co-optation most commonly refers to action performed in a number of fields whereby an opponent is nullified or neutralized by absorption but there are other distinct senses as well....

 and attraction. It can be contrasted with 'hard power

Hard power

Hard power is a term describing political power obtained from the use of military and/or economic coercion to influence the behavior or interests of other political bodies...

', that is the use of coercion and payment. Soft power can be wielded not just by states, but by all actors in international politics, such as NGOs or international institutions.
The phrase was coined by Joseph Nye

Joseph Nye

Joseph Samuel Nye, Jr. is the co-founder, along with Robert Keohane, of the international relations theory neoliberalism, developed in their 1977 book Power and Interdependence. Together with Keohane, he developed the concepts of asymmetrical and complex interdependence...

 of Harvard University

Harvard University

Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

 in a 1990 book, Bound to Lead: The Changing Nature of American Power.