It is just a variety name for a red chili pepper. You can use any of the long, skinny, dried red chili peppers.

Just all tomatoes don't taste the same but are all still tomatoes, all chili peppers have different flavors and different degrees of heat but are all still chili peppers.

New Mexico chili peppers have a mild heat level similar to Anaheims but are touted as having a "more earthy, smokey flavor".

Dave

I believe other names used for New Mexico chiles are Hatch chiles, and Anaheim. You could probably substitute dried Poblano peppers which are called Ancho.

ETA - yep, what Dave said.

Great information, thanks.