Voltage buffer arduino voltage sense
Roughly, your quote means that a buffers main purpose is to provide current sink/source capacity for a given output, translating to, for example, less susceptibility to noise and more tolerance to various loads.

Regarging your worries on affecting the voltage and fluctuations:







simulate this circuit &ndash; Schematic created using CircuitLab

As per Atmega328 datasheet, page 244, the Analog Input will be happy with an input impedance of 10kOhm or less.



Which means that if you manage to keep R1 and R2 in the few kOhm range you will be fine.

Note that the buffer cannot isolate the battery nor the resistive divider from fluctuations caused by the rest of your circuit, it will only "reproduce them" with higher current drive capability. So, if the load of the divider(Vbat/(R1 + R2)) is low enough to not affect the total load (which probably is the case), the buffer will be of little use.

In summary, make R1+R2 too large and they'll be susceptible to noise and charge the sampling caps slower. Make them too small and they might start loading your system a bit. (Although this second scenario is much less likely)