Thanks in advance for those who will help. :-)
The widget in question is Power Control, one of Android's default widgets. The icon you're asking about is Sync. As described in the page I linked to:
Press the Sync icon, second to the right, to cut the power to your Droid's Sync functionality. Sync keeps your contacts, email, calendar and other features readily available and constantly updated, which saves you time and effort when you're using your phone.