Hi,
I found an article in which the author build a Voltmeter prototype using ADS1115 (namely ADC with 16-bit resolution) and Arduino Uno.
This claims that we need to connect a large resistor in parallel with the read pins of the ADC (ADS1115), is this correct?
Yes
The ADS1115 can only convert voltages between -5 and +5 volts (in the differential mode).
So if you want to measure 12Vdc you have to use resistors to divide the voltage to a level the ADS1115 can handle.
The author suggests high value of resistance so the "voltmeter" does not add an significant load on the voltage to be measured.
@JohnRob
Thanks for your reply. You are referring to the so-called voltage divider, right?
I think that function should be fulfilled by R in the figure (the resistor connected in series with the unknown R).
What I'm confused about is the reason for the small "r" 
. The author claims that it serves as an internal resistor in the voltmeter, but I have not seen this kind of resistor in any other DIY examples using ADCs.
(Of course, I understand that it is necessary to use an appropriate internal resistance with the "analog" voltmeter/ammeter.)
Regarding the "r" resistor. I believe this is the equivalent input resistance of the ADS1115. You should be able to find it in their spec.
This resistor is so high that normally it can be ignored. However because the divider resistors are also very high it should be considered in the calculations.
I checked the references again, and it appears that "r" is not the equivalent input resistance, but an "internal resistance" that the author added externally.
I've attached another diagram, in which 1.2*2M[Ω] corresponds to r in the previous diagram, and In(+) and In(-) to M and N respectively.
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