Advocacy in this context has a wider sense than in the law college manuals. Think more "lobbying". Policy advocacy is the process of using information strategically to change policies or practice – for example public policy or resource allocation decisions within political, economic, social systems and institutions that affect the lives of others. "Using information strategically" means using it as a basis for evidence, logic, argument, and hence, negotiation. It is about changing or influencing the way decision makers see a particular issue, e.g. climate change, education, disability etc.
Principally it is Non-Governmental Organisations (NGOs) and charities that require policy advocates, but also private enterprise who want to get their issues supported by policy or legislation. Tobacco is a good example where you will have lobbyists on both sides of the debate. Increasingly NGOs/charities use this development approach to challenge local, national and international policies. Advocacy campaigns may typically contain elements of strategic analysis and planning for advocacy, evidence gathering, organizing and building civil society alliances - either through formal coalitions of organizations or informal networks of individual advocates, lobbying government policy makers (direct advocacy), strategic approaches to the mass media to build popular understanding and support (indirect advocacy) etc.
Also, see 'Charities, NGOs & Not-for-Profit'.