I'm a nerd, so the first thing I think of when I hear the word engage is Star Trek, the Next Generation. Forgive me.
That's now what this is about, sadly. Engaging is important to improv. It means interacting in an interesting/interested way with the people and environment around you. Engaging implies that you are actively seeking out ways to know, change, and learn from your environment.
In many scenes, actors want to see what other people are doing before they venture forth and begin to interact with the scene. For example, one character might be screwing in something, and another actor will wait and try to figure out what that person's doing before saying or doing anything. That's not engaging. That's being a passive observer, which is fine if your character is a passive observer, but not too interesting.
Engaging requires a ready, fire, aim mentality. The idea is that you shoot first and ask questions later (not literally though, since questions aren't usually good for improv). So, somebody's screwing in something (as in our example above)... instead of watching, start doing an action of your own, or contributing to his action, or endowing the "screwer" with some characteristic or objective.