1.) You can show them something. When we have a client who wants to engage parents it's the first thing we ask "what do you want to show them." Don't be scared to answer that. We had a detergent brand that wanted to show how effective it was on team uniforms so we offered to truck out washers/dryers to athletic games and practices to show moms on-site how well they cleaned. Couple that with a knowledgable on-site staff and some samples to take home and that is real engagement.
2.) You care about something they care about: children, schools, local communities. These two stats by Turnkey Intelligence are probably two of the most noted among field marketing firms. For good reason. When parents see a brand supporting a sport, a musical program, a STEM initiative, or creating their own initiative, it shows them the brand understands them.
3.) You can be relevant. Never buy a billboard again. Think about it: You put dozens of people to work on a billboard campaign and then buy a banner at a local high school. Most of the time it will cost you about the same to set up a partnership as it would to buy a billboard. One is a pop-up print ad; the other an emotional connection tieing you to the heart of a community.