As the title says; Can anyone explain exactly what recipes mean by saying “Make sure the curds do not mat”?

Yes.  As the curd is cooking, it loses moisture and becomes heavier than the whey in which it is floating.  It settles to the bottom and the mass of it tends to press into a mat.  You want to avoid this as the curd is losing surface area, will not expel the proper moisture and will not heat as evenly.

Aha! I figured it was something like that, thanks for the reply GCM. Off to attempt a stirred-curd cheddar!

Hope you have as good results as I had on the 4 month old s. c. cheddar I am just finishing up.  A delightful cheese.  Do you have a pH meter?  It will help you immensely.

We currently do not have a PH meter, hoping the cheese turns out OK without it. A PH meter is currently on our “wish list” of cheese paraphernalia =)

Edit: Curds have been pressed for about two hours now, so far it’s looking OK. Another 24 hours of 50 lbs. of pressure, we’ll see!