Public engagement is ‘intentional, meaningful interactions that provide opportunities for mutual learning between scientists and members of the public’ (Nisbet & Markowitz, 2015, p.2), and is generally considered to be (or is aiming to be) a two-way dialogical process between science and society. However, it's not a universally understood term, and is sometimes used synonymously with science communication, or outreach, or other phrases. 

I've written a blog post about Science Communication terminology that might add clarity.