The Recent Activity section allows you to add or shows you all the transaction and changes you have made for the last 7 days under Program Groups, Programs, Accounts, Contacts, Notes, Registrations, Invoices, Payments and Memberships. It also allows you to directly search for or add new Program Groups, Programs, Accounts, Contacts and Notes.
In this section, you will see a chevron icon 
which makes the Recent Activity section be visible or hidden in the Home Page.
In the Show Activity Since dropdown box, you are able to select from the dropdown the days which there were changed made in the different areas of the system.