Water dripping out of small pvc pipe in soffit of house
I'd suspect it's a secondary drain. It's possible that the main drain was simply overwhelmed, and the condensate level backed up to the point of the secondary drain.  If it was really humid, a large volume of water could have been removed from the air.  If the main drain is slow, it could have simply not been able to keep up.

Without inspecting the system, it's impossible to say for sure what's going on. If you can follow the pipe back to the air handler, you could confirm that it's the secondary drain. You may also be able to determine if the main line is clogged, and possibly fix it.

If you go poking around, you could post some photos here, and somebody might be able to offer more help.

From the looks of the pipe, it doesn't look like it would cause any water damage.  But I can't see if it's dripping on anything important.