Admin can set discount rules for some specific customers ( he can choose customers for this rule according to some specific conditions like For how long a customer is registered on his site, How much a customer spend on his site, Number of visits in a particular month/year, Number of product he purchased from his site, Role of the customer, etc ).

For making this discount rule select Rules for Specific Customer tab.
Now click on Add New Rule.

Fill Rule, Restrictions and Validity tabs accordingly.
After saving the rule it can be seen in the given table below.
You can enable or disable this rule from this page only.

Now if you enable Rule permission as above your Rules are active and if any customer who match all your cart purchase something from your store he/she will get discount according to your settings.