Hi Gary. You can do a lot lot of drills in the pool and obviously doing one armed swimming is one of them. All drills have an end goal of improving your overall stroke and therefore speed and endurance in the water. Doing one armed drills enables you to focus on catching the water properly, lengthening your stroke, and getting good body roll.
When you swim your body motion through the water can be a combination of yaw (sideways zig zag), pitch (up and down), and roll. The only good motion is roll as yaw and pitch increase frontal surface area and therefore drag which slows you down. Yaw comes about through overeaching and poor hand placement in the water along with general inflexibility. Pitch is caused by lifting your head to breath rather than rotating the head sideways. This causes your bum to drop.
Roll is important because it enables you to breath properly, but more importantly it increases your stroke length markedly. Watch some of the replays of Phelps et al from the recent Olympics, especially the underwater shots.
So back to one arm swimming. The basic drill is to extend one arm straight out in front and swim with the other. In this drill you should swim on a 45 degree angle. This puts you into the roll position, enables you to breath easier, allows you to watch how your hand comes over the top and enters the water, and allows you to complete a full extended stroke. You should do say 25m at a time and then swap sides. You may want to do 25m, 50m, or 100m intervals depending on what pool you are in and how fit you are. Harder versions of one arm drills are catch-up and breathing to the non stroke side. In breathing to the non stroke side, the non stroke arm is by your side and not extended. This drill really puts the heat on you to roll otherwise you will find it hard to breath. With catch up you extend one arm out in front, swim with the other arm, touch the extended arm, and then swim with the other arm. In other words its like normal swimming but you can't start stroking with the alternate arm till both hands touch out in front. Don't cheat by going early as it negates the purpose of this drill. This focuses you on getting a good powerful catch up front and accentuates the need to roll in order to get good stroke length. With catch up you can do longer repeats of say 100m, 200m, 400m.