To some extent, the lifeblood of improv comedy. The audience may be asked for a location, a relationship, an action, an object, something about themselves, or just about anything! The goal is to provide a seed for the rest of the show.
Some groups use audience suggestions to proove the audience that the show is not scripted. Others, notably within the Impro Match franchise, do not involve the audience at all. Really, if the audience does not want to believe the show is improvized, then the use of audience suggestions will not convince them.
There is some debate as to whether the host should religiously take the first suggestion received, or would be allowed to "fish" for a good suggestion. We suggest you do what suits your style best.
See Ask-for for a list of questions to get suggestions.