I have heard this twice today referenced to batting. What is it?

Scrim is what they use to attach the cotton fibers to, this keeps the fibers from migrating around.

I bought a very loosely woven fabric for curtains one time that they called scrim... kinda like cheese cloth

In battings, it is a thin piece of fabric through which the batting is needle-punched. Needle punching batting makes it more stable. Needle punching batting through scrim makes it even more stable.

Warm n Natural is an example of a batting that is needle-punched through scrim. It is very, very stable so needs to be quilted only 10" or so apart, or a quilt with this kind of batting can be tied. Scrim can give a batting a slightly more stiff drape.

My favorite batting is Mountain Mist Blue Ribbon 100% cotton, a very old-fashioned batting that has been in use for many decades. It is not needle punched and therefore needs to be quilted about every 2". It would not be a good batting to use in a tied quilt, because the batting would have a tendency to ball up with washings and use. It needs close quilting to keep it in place. I love it, though, because it becomes softer with every washing. After about 10 years of hard use, a quilt with this batting is soft as a cloud!

Picking batting is always my hardest part, so many to choose from!

Is the scrim on both sides of the batting? If so, should the scrim be on the top or bottom of the quilt or doesn't it matter?
Thanks!

As far as I know there is only one layer of scrim (a "net" of polypropylene fibres) where the cotton is needle-punched through.