It measures from GND
The block does not measure between its two screws in the way a multimeter does. It measures the + screw from your board's GND, because its GND screw is your board's GND. So the minus side of what you measure must be joined to it, and a part whose ends are both above GND cannot be measured by clipping across it.
A voltage is always from somewhere
A voltage is a difference between two points. A multimeter measures between its two probes, wherever they are, because its probes are connected to nothing else. This block has two screws too, but they are not like probes. The GND screw is the same copper as the header's GND pin, and so the same copper as your board's GND.
So the block measures one thing only: how far the + screw is above your board's ground. That is the source of every surprise below.
Four wirings
Both screws, on something with its own two terminals. A battery, a bench supply, a solar panel: plus on the + screw, minus on the GND screw. The GND screw joins the battery's minus to your board's ground, the two share a zero, and the reading is right. This is the wiring for almost everything.
The + screw only. The battery's minus goes nowhere, so there is no loop. No current flows through the resistors, and the bottom one holds SIG at 0 V. The sketch reads zero from a full battery. A source that shares no ground with your board is said to be floating, and floating things cannot be measured until something joins them to GND.
Across a part. This is the one people wire. The circuit is already on your board's ground, because one supply powers both. Putting the screws across a resistor whose lower end is not ground connects that lower end to ground through the GND screw. The part underneath it is now shorted. The sketch reads a number, and the number describes a circuit you changed by connecting to it. With a stronger supply that short can overheat a wire.
Two readings. To measure across a part whose ends are both above ground, measure each end from GND and subtract. One block and two readings with the + wire moved between them, or two blocks side by side, both with their GND screws on GND.
The rule, once
The GND screw only ever goes to the ground of what you measure, the same point your board's GND is, or will be, joined to. If the circuit already shares your board's ground, the GND screw may go there or stay empty, and nowhere else.
When it does not work
Check that the battery's minus is on the GND screw, not only its plus on the + screw. With the minus left off there is no loop, no current flows through the resistors, and SIG sits at 0 V. The battery still has its voltage between its own terminals; the block cannot see it.
Not by putting the screws on its two ends, unless the lower end is GND. The GND screw is your board's GND, so it pulls whatever it touches to ground. Measure each end from GND instead, one reading each, and subtract.
Yes, and the GND screw does it for you: once the circuit's minus is on the GND screw, the two share a ground through the block. What you must not do is also connect some other point of that circuit to your board's GND, or you have joined two different points together.
Measure each junction from GND: the first block across the bottom battery, the second from the top of the stack to GND, and subtract. Two blocks with their GND screws on different points would join those points through your board's ground and short the battery between them.
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