When creating a report, the "Last Activity Date" filter includes status updates, notes, events, tasks, dropbox emails, mail merges, and phone calls placed with our Click-to-Call feature. The Last Activity Date does not include synced emails, but it should include synced calendar events if they are directly related to the contact. It also doesn't include workflows.
Below is a screenshot of the sample report entitled, "Clients with no activity in the last 30 days":
Reporting fields such as the Last Event Date and the Last Note Date (which are included as part of the last activity) are relevant to the contact that they are related to. For example, if you have an event that is related to an individual, it's not going to count toward the household's Last Event Date unless it is also related to the household record directly. The last activity fields in a report will only reflect the contact(s) to which it is directly related. It does not include the activities of related contacts.