If you need to restore an activity that has previously been marked complete within your database, there are a couple of ways to accomplish this.
If the activity was not attached to a contact record, you would need to restore it from your main Calendar. From the Actions menu above your calendar, click Show Completed:
All completed activities within the date range you are looking at will then be on display. You can then click the Activity you want to restore to view its Activity Details. On that page you will then see an Actions area, where you can click Uncomplete to restore it to your Calendar:
If the activity you want to restore was attached to a contact record, you can restore it in the manner above. Alternatively, you can go to a contact record's Completed Activities area to do so.