The end connection of a fitting that is to be assembled into another fitting is called the “Spigot.” The spigot end of a fitting has the same outside diameter as pipe. The common female connection of PVC fittings is referred to as the socket or hub, and the spigot end of a fitting can be inserted into a Hub or Socket.
The valve has both spigot and socket connections. PVC pipe slips into the smaller socket connection and a PVC coupling slips over the larger diameter outside spigot end.
The check valves last a long time as long as they're not near a tab feeder. If they fail, the top can be unscrewed and the guts replaced. I'm pretty sure that yours are CMP, but verify by looking for markings on the valve.
When you look through the clear top, you can see the spring and flapper assembly. The flapper should move up on the hinge as water begins to flow and it should go back down as the water stops flowing.