One fifth

Two resistors in a row

The + screw goes to the top of a 30 kΩ resistor. Its other end goes to the top of a 7.5 kΩ resistor, and that one's other end goes to GND. SIG is the point where they meet.

There is one path through them, so one current flows through both. At 9 V on the terminal it is 9 V divided by the 37.5 kΩ total, 0.24 mA. Ohm's law then gives each resistor its share: 0.24 mA through 30 kΩ is 7.2 V, and through 7.5 kΩ is 1.8 V. SIG is the voltage across the bottom one, 1.8 V.

Why it is one fifth

The shares follow the resistances. The bottom resistor is 7.5 out of 37.5 kΩ, which is one fifth, so it gets one fifth of the voltage, whatever the voltage is. The current does not matter; it cancels out.

SIG = input × 7.5 / (30 + 7.5) = input / 5

So a sketch reads SIG and multiplies by five:

input = SIG × 5

That is the whole of the block. The front of the board says 5X SCALING, and the voltage divider works through the same arithmetic for any pair of resistors.

What sets the accuracy

The ratio is only as good as the two resistors. Their part numbers mark them as ±1 % parts. If the top one is 1 % low and the bottom one 1 % high, the ratio is about 1.6 % above a fifth; the other way round, about 1.6 % below. Most boards will be closer than that, but a sketch that trusts the five blindly can be off by a fifth of a volt at 12 V.

Your board's side adds its own error: the reference voltage an Uno measures against is its 5 V supply, which is rarely exactly 5.00 V. Calibrating and averaging takes both out with one number measured once.

What it does not do

The divider divides. It does not limit, clamp or switch off. 25 V on the terminal is 5 V on SIG, and 50 V would be 10 V. Nothing on the board notices the difference, which is why the limit belongs to your board and not the block.