What is it?

[Michael Thomas]

Hot water supply is at lower left, pipe at lower right goes to hot water side of laundry tub faucet.

Pipe at upper right dives behind drywall and could not be traced.

(I did NOT pull the pin...)

[Rick Cantrell]

I'll say a pressure relief valve.

[wayne soper]

Air vent

[John Arnold]

water hammer arrestor?

[Rod Butler]

Let me add to the speculation. Two lines in and one out would make me think it is a mixing valve. Not sure about the why, but the installation seems to make sense.

[Garry Blankenship]

Pretty sure that came over on the Mayflower. All you need is the manifest.

[H.G. Watson, Sr.]

water hammer arrestor?
Ding Ding, pass that man a cigar (or a biscuit).

In IL, still needs air chambers for that laundry faucet even end of run. Appears to be lacking (typical) in the "protection from freezing" department.