Average widgets show you the average value of a certain metric for a given period. Those widgets include a trend as well.
Average widgets are not available for all metrics. You can use them with the following: Users, Sessions, Session length, New users and Exception occurences.
Let's take the Users metric. If a date period of [Jun 12, 2011 - Jun 19, 2011] is selected then the widget will show the average number of users for this period by basically calculating the sum of the users for all days in that period and then dividing it by the number of days.
Average widgets display a percent formatted number called trend. It shows the difference between the average value of the currently selected period and the previous period with the same length. So if we select the same period as the example above then the previous period with the same length would be [Jun 04, 2011 - Jun 11, 2011]. The trend shows how many percent the average number has increased or decreased between the two periods.