soft power is a way of dealing with other countries that involves using economic and cultural influence to persuade them to do things, rather than military power.
Oxford Learner's files the term under politics, and the Cambridge Dictionary marks it as specialized political vocabulary, defining it in parallel terms as the use of a country's cultural and economic 📝influence to persuade other countries to do something, rather than the use of military power. Both dictionaries direct the reader to compare it with hard power.
A broader definition appears in the Collins English Dictionary entry reproduced on Dictionary.com: the ability to achieve one's goals without force, especially by diplomacy and persuasion. That entry also points to hard power for comparison. Where the learner's dictionaries speak of countries, this wording describes the 📝power to reach goals without naming any particular kind of actor.
Recent news sentences quoted on Dictionary.com apply the term to a royal state visit, to the transformation of a football club, and to India's "soft power" through yoga, tourism and handicrafts.