what voltage level is a digital low for the interrupt mode LOW? I am learning about interrupts and one of the interrupt modes is LOW which triggers anytime the pin is a digital low.
Can someone tell me what voltage that is for an Arduino nano? I did a google search and it said a LOW can be anywhere from 0 to 2V.
I am making a project using a nano and I am powering it with batteries. It would be great if I could set up an interrupt to turn on an LED when the batteries were getting weak so I would know when to change them.
It would be great if I could set up an interrupt to turn on an LED
when the batteries were getting weak

That won't work. The thresholds for the pin registering LOW or HIGH
depend on the supply voltage. Very roughly:

a pin in guaranteed to register LOW if its voltage is below ⅓ Vcc
it is guaranteed to register HIGH if it's above ⅔ Vcc
nothing is guaranteed between ⅓ and ⅔ of Vcc.

For the exact voltage levels, you should check the datasheet.
Note also that those are guaranteed levels. The actual thresholds are
closer to ½ Vcc, with an hysteresis of roughly Vcc/10.
For detecting a low battery condition, you should use the ADC, combined
with either a voltage divider on Vcc or the internal bandgap reference.