"Critical access hospital" (CAH) is a designation/category established by CMS (the federal government). CAHs are small, rural hospitals that meet specific criteria for how far they are from the next nearest hospital -- basically, people in their area would be entirely without hospital services (within a reasonable distance) if the hospital wasn't there. There are also requirements about the maximum number of beds (25) and maximum average LOS (96 hours) they're allowed to have. CAHs would not take more complicated cases (or would transfer those people ASAP to a larger, better equipped facility). Because they fall into this category, they aren't required to meet the usual CMS COPs and are held to a lower standard by CMS -- for instance, CAHs aren't required to have an RN in the hospital 24 hours a day (they just have to have one on call at night). (That doesn't mean that CAHs don't have one or more RNs on duty 24/7 -- just that they're not required to.)
Basically, these are small, rural hospitals with basic, limited services and staff only and short lengths of stay that would treat only fairly simple cases.