Outlook connects an online version with the email address you use to set up Office 365. You can see a desktop Profile that you can set up through your Control Panel or local Outlook to connect to the site (see Figure 2).
Figure 2 Outlook can connect locally to the online location by adding an Email profile for the Exchange server identity you create for Office 365.
With the installation established, adding a contact in either the desktop or online puts in a corresponding entry in the other location (see Figure 3).
Figure 3 Outlook in the cloud connects contacts with the local installation.
Similarly, you can coordinate Outlook calendars between the desktop and the online version of Outlook (see Figures 4 - 6).
Figure 4 You can create an appointment in Outlook on your Office 365 site.
Figure 5 The new appointment appears in your online calendar.
Figure 6 Moments later, the appointment is also visible on your desktop.
The one drawback in Outlook that I can see so far is the inability to easily and directly add users or contacts, or calendar items, from a desktop PST file to the online folder.
You can, however, import items from a *.CSV file that you create from Outlook, or another contact management program; you can use such a file in the Admin area (described later) to add users to your SharePoint site as well.