Help figuring out what this piece is

I just moved into my place and when water is put into the right sink it sprays out of that rubber hose shooting off of my pipes. Ive never seen anything like this piece before and not being a plumber I have no idea what it is. Can someone help me understand what this piece does and is it supposed to be open and just hanging like that? It seems like ofcourse water will spill out of it the way is sitting open.

The previous homeowner took their "Reverse Osmosis" water filtering equipment when they moved out. That tubing that was cut was for draining the brine.
Those things run about $250 and more.

You will need to remove the tee with the tubing. Just pick up some new pipe and fittings for under the sink.

Because they drilled a hole in the vertical black pipe to tap into, you will need to do some pipe replacement here. Go to the hardware store and ask for an "end outlet waste kit"...it will have everything you need.

By the way, the small gray tube leading off to the right may also end up in a "surprise" somewhere. You need to check this all out.

Thanks so much Terry! Very helpful.

The white/gray tube is the feed to the old RO unit, and it was probably also just "cut off", although it might go to the refrigerator's ice maker. If it is not connected to something, he can remove the gray tee and reconnect the supply line to the nipple on the other side. It would be the "easiest" way to do it, but NOT how I would do it.

Looking at the supply lines from the wall shutoffs, they are the corrugated kind that are integrated with the shutoffs. I don't reuse those. Any bending of those can cause them to crack. I would replace the shutoffs at the wall while you are under the sink removing the drain fittings for the "removed" RO.