My colleague Gail Griffith and I did a preconference at ALA called Mental Model Busting. One of the mental models we explored was community engagement. As you might guess, people’s mental models of community engagement were all over the map. Not that there was disagreement, just wildly different assumptions about what is meant by “community engagement”. The flipcharted responses revealed that to some it was partnering, for others it was identifying community. For some it was having the whole community read the same book, for others it was letting the community see our value and for others it was just “messy” ;) 
If you want to get your library involved in engaging your community you may need to have a mental model busting conversation with your staff. Why does it matter? Because your mental model determines how you expend time, money and resources. For instance if your goal is to “let the community see our value” you might hire someone to beef up your PR efforts. If “finding partnerships” is your goal you might prioritize your time looking for partner opportunities outside the library. If “having the community read the same book” is community engagement, you might say “We’re already doing it!”
The process of surfacing mental models exposes a group to the fact that there are multiple concurrent realities and that there is not one correct answer. This allows people to see for themselves where they might be limited in their thinking. Instead of convincing people that they are wrong and you are right, the conversation should allow people to hear different perspectives and bust up their assumptions. If you can create the right atmosphere where people are really listening, they’ll be able to find their own limited thinking and learn from each other to create a shared, and presumably much broader, view of community engagement. The point of the exercise is not to figure out who is right and who is wrong or to more perfectly define community engagement. The goal is to figure out what decisions should be made about spending our limited time, money and resources so the library can have an impact on community engagement.