Find the Activity that you wish to complete and/or close. Note its status.
To complete the activity, i.e. when it has been implemented, click on the Complete Activity button
This will update the Completion Date to the current date/time and the Completed By to the user currently logged on
To close an activity, i.e. shut it down completely, click on the Close Activity button
You will be asked to confirm your selection.
This will then update the Closed Date to the current date/time and the Closed by to the user currently logged on
Going back to the list of Activities, you will see that this has updated the status.