You may delete or "undo" an activity only if it is the original version. You cannot undo an activity that has an activity note attached to it. Undoing an activity can only be done by the author of the activity within a day of the original creation. After that time you will need to complete or drop the activity.
To complete an activity: Use F15
To drop an activity: Use F10 (change) and than F16
All completed and dropped activities remain on the contact record as history.