-Reading the voltages at a point between R1 and R2 let's you know the resistance values for R1 and the parallel combination of R2&R3.
-Knowing that you can calculate the current through the circuit.

I don't know what it means to read the voltages (plural) at a point.

For what you have in mind, if I have a voltmeter where would I put the red (positive) lead and where would I put the black (reference) lead?

The only thing that makes sense to me is that you mean measure the voltage at the node connecting R1 and R2 relative to the negative terminal of the supply -- in other words, measure the voltage across the parallel combination of R2 & R3.

So let's say that I do that. I have a 10 V source and the voltage is 5 V.

What is the resistance value for R1?

What is the resistance value for the combination of R2&R3?

 

Reading the voltages at a point between R1 and R2 let's you know the resistance values for R1 and the parallel combination of R2&R3.

All that tells you is the relative value of the resistances, not their actual value.
Remember you can only measure one current and one voltage (besides the supply voltage).