SharePoint 2013 supports connection to MS Outlook application in order to collaborate and coordinate activities and projects and to improve business efficiency and productivity, especially if you work offline and don’t have instant access to your SharePoint sites all the time.
You can synchronize information in two directions for items in Contacts lists, Calendars, Tasks lists.
But you should keep in mind that, unlike Contacts and Calendars, syncing SharePoint Tasks with Outlook relies on the installation of Exchange Server 2013 within your organization.
SharePoint Server 2013 and Exchange Server 2013 must both be installed in the same environment. Otherwise, you will not be able to accomplish this, in spite of the “Sync to Outlook” button will still be active.