The main purpose of the Mundell-Fleming model is to determine equilibrium income and how this income responds to economic policy and shocks. It merges the foreign exchange market (FE), the goods market (IS) and the money market (LM). Overall equilibrium obtains when these three markets are in equilibrium. Viewed in a diagram, equilibrium is where FE, IS and LM intersect.
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The Mundell-Fleming model refines the IS curve by tying down two loose ends. The IS curve tells us that equilibrium income depends on the interest rate. As long as we do not know the interest rate (which is an endogenous variable) we have not really determined income. Also, since the position of IS shifts when the exchange rate moves, equilibrium income depends on the exchange rate too. If we do not know the exchange rate (another endogenous variable), we cannot determine income (even if we knew the interest rate). The foreign exchange market and the money market, which the Mundell-Fleming model adds to the goods market, serve to determine the interest rate and the exchange rate. This finally permits us to nail down equilibrium income.
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What if the three curves do not intersect in a common point? Do not worry. They always do. The reason is that only two out of these three curves are fixed by the policy maker and/or exogenous variables. The position of the third curve depends on endogenous variables as well. These endogenous variables always adjust so that they move this third curve into the position where the other two curves already intersect. So the third curve is actually redundant. You may forget about it, for it is always where the other two curves are, just as the tail is always where the dog is.
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Which one is the third, redundant curve? And which are the two we need to keep our eyes on? Well, that depends on whether we operate under flexible exchange rates or under fixed exchange rates.