Basic Question Regarding Forks for a Mountain Bike
 

What do the millimeter measurements for forks with suspension refer to? For example, on this site both 80mm and 100mm models are available. I've also seen listings in which the measurement is a range, such as 115-160mm.

That's the fork's suspension travel, how far it can telescope. The travel on some models can be adjusted on-the-fly (Fox TALAS, for example) while others like my RockShox SID must be disassembled and a part added or removed in order to change the amount of travel.

If you'd read the next word after the 80mm; Travel, you'd have answered your own question. it's the travel, or the amount the fork can move up and down on bumps and such.

What forks do you currently have, and what are you looking to replace with?

As mentioned, the mm = travel, what you need is determined by the frame you have, some are designed to have longer travel forks than others.