Hi Penny
You don't have to worry about doing this. Let me explain, every time you log into your admin it will record this activity, then for every other click and page you visit in your admin it will also record this activity. So you can see this activity log can soon clock up some entries into the database.
I wouldn't worry about emptying it, I do mine all the time. It's just a log of the activity in the admin, it won't delete any inportant info about customers or counters etc.
I hope this helps.
Thanks
Phil
PS Have a look at this
http://www.zen-cart.com/forum/showthread.php?t=63579