You must have the following rights to close a discussion (check with
your Admin to makesure you have it):
-Add and Customize Pages
-Manage Lists Manage Lists

You can do the following:

On the site, click Site Settings.
On the Site Settings page, under Administration, click Go to Site
Administration.
On the Site Administration page, under Management and Statistics,
click Manage Web discussions, and then do any of the following:
To see all discussion threads associated with your site, click All
Web discussions, and then click Update.
To see discussion threads filtered by a particular URL, type a path
in the Web discussions  in folder http://server_name/ box, and then
click Update.
To view a particular discussion thread, click the URL for the thread.
To delete/closed a particular discussion thread, select the check box
next to the thread, and then click Delete.
To delete all discussion threads on your site, click Delete all
discussions.