Back in the dark ages, divers that needed more gas than could be carried in a single tank began strapping two tanks on their back in what is called an "independent doubles" configuration. Each tank has it's own valve and regulator and there is no connection between them - they just sit side-by-side on the backplate. Divers with independent doubles have to alternate between regulators in order to access the gas in the separate tanks, but it mostly works. There are a number of drawbacks to diving with independent doubles, including the futz factor associated with switching between tanks. Many divers found that the changing bouyancy characteristics resulting from one tank becoming lighter as they breathed it down created problems with list (or roll, depending upon your lexicon) and that they had to switch back and forth regularly to maintain good trim.
Thus, the idea of connecting the two tanks together via a manifold was developed. The manifold is simply a tube connected to both tanks that allows gas to freely pass between them. It bypasses both valves on the tanks (what is often referred to now as the left and right post) and is not affected by them - turning off either post will not shut the gas flow off through the manifold. Most divers liked this much better than the independents they had been using but it didn't take long to discover a major potential problem with the manifold: in the event of a valve failure, there was no way to prevent the loss of all of your gas.
Generally, a massive and sudden loss of gas is considered to be a bad thing and a solution wasn't long in coming: add a third valve to the system, in the middle of the manifold, that would allow the gas flow between tanks to be shut down. This valve would allow each tank to be isolated from the other, effectively returning the system to a set of independent doubles. In the event of a valve failure, shutting down the isolation valve will allow you to keep half your gas. These days, almost all manifolds sold have an isolation valve in them. Standard procedure is to leave the isolation valve open except during shut-down drills or in the event of an emergency.
It's all kind of circular but that's the point. In some instances, independent doubles are the best solution, in others you want the tanks to function as one. The isolation manifold allows the diver to choose which is best. It also give doubles divers something new to argue about - what is the proper sequence for a shut-down in the event of a failure, but for more about that argument you should visit the technical forums.
