Agents with "common sense" are ones that are not necessarily very good at any particular task but that are able to maintain a focus, an assessment of what the task or topic is, or that it has changed, or that it is not clear, that help is needed, that the task should be given up, etc. A familiar human setting is that of trying to follow an expert discourse, or perhaps a discourse in a foregin language, and missing a lot of the details: the agent knows that it is not following well, and that there are things it can try to deal with this (asking questions, getting a translator, giving up altogether).
An example of what might be worked on is an intelligent workstation that can enter into a dialogue with a user, and reason on the fly about that ongoing dialogue: changes in topic; changes in meanings; miscommunications; new expressions; calls for clarification; ambiguous, contradictory, or meaningless expressions; nonexistent entities. The goal is not only a highly useful contribution to automated reasoning engines, by also a better understanding of the detailed nature of reasoning in general, and especially of knowledge and inference mechanisms involved in ongoing reasoning in an agent with a lifetime of its own rather than a one-time task performance.
(Another even more ambitious example is all the above but in an autonomous mobile robot.)