The top A/C drain in my attic is leaking. Why?
On many air handlers, there are two drain outlets.  The lower drain hole is the "regular" drain that is typically hooked into the house's drain pipes somewhere.  You don't see it working - it just silently drains out the condensate water.

The upper hole is an overflow.  It's normally routed to a pipe that will drain out of the eaves of the house or another visible location.  When you see this dripping, you know the main drain is clogged.  This secondary drain can also be fitted with a switch that cuts power to the A/C so the overflowing drain doesn't damage anything.

So, the answer is that the lower, normal drain is clogged, probably with some mold/mildew that collects on the side of the pipe.  If the water is flowing at all, bleach or a mild drain cleaner can be used to try and break it loose.  If there is no water flow, compressed air into the pipe (carefully) can be a good option.