Public engagement involves activities that bring researchers and the public together. It is more than just meeting an audience and telling them about your research - effective public engagement is about two-way communication, with the researchers listening to and learning from participants. Research Councils UK provide a comprehensive definition (RCUK PDF) on their website.
Activities can range from engaging people with social science concepts through staging debates to involving key stakeholders in shaping research priorities and directions.
Done well, public engagement can build trust and understanding between the social science research community and a wide range of groups, from policy makers through to school children.
Public engagement can help you strengthen your research questions or improve the response rate to data collection methods. It can also build on and support the wider activities of your strategy.