cup-thing on the side of furnace and pipes going into it

Hi there.

What is the cup-thing on the side of the furnace? It is full of water and overflows into a drain pipe.

I think the flexible black pipe is from the AC. It drips water. Should it be placed into the cup as shown in the photo?

What are the 2 white rigid pipes above the cup (not the drain pipe)?



Thanks so much!

Paul