Kitchens – Water Dripping out of Overflow Pipe outside of house near the kitchen

I would remove the internal hose, and inspect it for damage. Also inspect the connection between the hose and the wand head.

High efficiency furnaces will make condensate. They run the air back through the hot exhaust to get more heat out. This also cools your exhaust enough to use PVC - that's what your upper line is.

In the process of cooling the exhaust, you might get some condensation. Typically that's collected in a little sump tank. When the sump reaches a certain level, a little bitty pump pumps it out - that's your lower line.

If it freezes where you are, you might want to insulate that lower line. If it freezes shut, your sump could overflow in the mean time. It's just a dribble of water, but still. It's a leak of water in your attic.