The probe gets plugged (screwed)into the monitor you have you have hanging on the tank stand. Hard to tell for sure, need a bit of a close up. Different brands of probes can attach differently.
The other end of the probe (clear plastic end with some liquid in it) is hung in the water of the tank, and the digital readout will tell you the pH of the tank water, relative to its temp. Don't hang it in a bubble stream, but a little water movement around it is not a bad thing.
I believe the bottle of liquid, in the probe box, is a solution the helps the probe determine pH. If the probe is dry inside, it won't work, it needs to contain the liquid to do its job.
You may need to regularly calibrate the monitor with a couple known standard pH solutions.
I usually use a pH 7.0 standard, and pH 10 standard to calibrate because my water is normally on the basic side, but if yours is a bit acidic, you may need a pH 4.0 and pH 7.0 standard.
The other UXB type cord gets plugged into the digital readout box, and then into your computer, and will (with the right program, and regular testing) allow you to watch pH trends, and is an aid to help determine when you water is becoming acidic and you need to do a water change. If the pH is 7.5 after a water change, but drops to a pH of 6.5 in 2 days, then you need to change some more, because the uric acid from fish urine and decomposing food has overwhelmed the tanks buffering capacity, and turning acidic.