You mention that it's a jet pump - so the valve is probably for priming the jet. The centered pipe is suction, the off-center pipe is the jet feed.
In my opinion, jet pumps are well on their way to being a holdover from times past, when electric motor reliability was questionable, and submersible electric motor reliability doubly so - they trade complexity and inefficiency of operation to keep the motor out of the well - a portion of water is pumped down to the jet, to help bring up more water from a depth where straight suction won't work. As such, when starting one up, you need to put water into the jet pipe (without having a working pump...complex, not fun.)
With current technology, when time comes to replace a jet pump you will almost always save considerably on operational costs by changing to a 2-wire deep well submersible pump with a single output pipe. However, it's generally not worth doing that if your jet pump is working well at present.