In a normal engine using poppet valves, the valves are opened by the camshaft pushing down on the top of the valve, often via a long pushrod and rocker taking the power from the crankshaft area to the top of the cylinders. The valve closes itself when the cam stops pushing on it, using a spring.
The problem with this system is that as the RPM of the engine increases, the speed at which the valve closes must also increase, and that requires a stronger spring. In addition the "perfect" design requires as large a valve as possible for easy airflow, but a large valve requires considerably more force to open due to the pressure against it inside the cylinder. These changes would require a stronger camshaft, and considerable energy to run it. At some "magic number" it would seem that all of the energy of the engine would go into the huge camshaft needed to push the huge valves and their equally huge springs.
The sleeve valve avoids all this. As the name implies, the valve is constructed as a sleeve, one that fits around the piston inside the cylinder. Several ports (holes) in the side of the cylinder replace the more normal intake and exhaust ports on the head. Similar holes in the sleeve open and close the ports like a poppet valve would, but do so by being rotated into position. The sleeve has a gear ring on the bottom that runs in a channel, and a small cut in the cylinder wall exposes the gear so that the sleeve can be turned.
There is no need for a spring in the sleeve valve, and the power needed to operate the valve remains largely constant with RPM – so the system can be used at very high RPM, and with no penalty for doing so. Furthermore it does away entirely with the camshaft, pushrods and rockers, replacing them all with a single gear running directly off the driveshaft. For an aero engine this sort of simplification and weight savings is an engineer's dream.
Another advantage of the system is that the actual size of the ports can be easily controlled. This is important when the engine runs over a wide range of RPMs, because the speed at which the air can move into and out of the cylinder is defined by the size of the tubing, and does not vary linearly with RPM. In other words at high RPM the engine typically wants larger ports that remain open longer, which is very easy to arrange with a sleeve.
Less important advantages include leaving the cylinder head empty so the spark plug can be placed wherever is best, the valve is not being continually "hammered" into the port leading to rapid wear, and the exhaust's heat is spread evenly around the cylinder, rather than generating a hot spot on the exhaust valves. Hot spots in engines must be avoided, they can often lead to the destructive problem of knock. In the sleeve valve engine this is not an issue, so they can be run at higher compression.
The sleeve has one major disadvantage though, and that is that it can't be sealed well. In a normal engine the piston is sealed into the cylinder with rings, and after a "breaking in" period any imperfections in one is scraped into the other. The result is a tight fit. This sort of fit is not possible on the sleeve valve however, because the piston and sleeve are moving in different directions. In the 1940s this was not a major concern because the poppet valves typically leaked anyway.
A number of sleeve valve engines were developed starting with a seminal research paper by the RAE, published in 1927. This paper outlined the advantages of the sleeve valve, and seemed to suggest that poppet valve engines would not be able to evolve much beyond 1500 hp. Napier and Bristol started developments of sleeve valve engines that would eventually result in the two most powerful piston engines in the world, the Napier Sabre and Bristol Centaurus.
After the war the sleeve valve rapidly disappeared. As it turned out the problems with sealing and wear on poppet valves were remedied by better materials, and soon the poppets were sealing very well indeed. Oil leakage dropped almost to zero, and the power used by the springs and camshaft was a small price to pay for such a tight seal. The problem with oil leakage in the sleeve is much more "built into" the system.
Recently the sleeve valve has started to make something of a comeback, due largely to the same sorts of improvements that led to its demise. Newer materials, and more notably newer and dramatically better construction techniques, can make a sleeve valve engine that is so "tight" that it leaks very little oil. However most advanced engine research continues to look at entirely different designs, like the rotary engine, as opposed to more conventional improvements like the sleeve.