Just got in from a family wedding, so I may not make much sense, but here goes.
The easy way to look at this is that until the pilot operated check valve sees "X"psi on the intake side of the cylinder, it does not open the exhaust side of the cylinder and allow fluid to exit that side. (It is important to block the exhaust side when attempting to hold a given position because with the intake only blocked, the cylinder can still move by pulling a vacuum (negative pressure) on the intake side. This is really a bad thing as contaminants can be pulled into the system and seals can be damaged by the generation of a great enough vacuum.) This means that there must be pressure from outside of the cylinder (which normally would only come from the operator opening a valve) before the cylinder can move. The "dual" part is important because in a 2 way cylinder either port can be the intake or exhaust, depending on which way you're trying to move the rod.
The whole idea is to isolate the hydraulic pressures inside the cylinder caused by forces trying to extend or retract the rod and only allow movement when the operator wants it. Clear as mud now - right? /forums/images/graemlins/laugh.gif