First let's restate the basic premise. Look at all the unsolved cells in a row (or column or region). Look for two of these cells that have exactly the same two possible solutions. If such a pair is found, then all occurrences of these possible values can be eliminated from the other unsolved cells in the same row / column / region.
Why should this be so? The simplest way to show this is with an example. Suppose we have this situation for a set of nine cells.
Our exclusive pair (1,9) appears in cells 1 and 5. So why does this now preclude 1 and 9 from being solutions to other cells? Well, suppose 9 was the solution to either cell 8 or cell 9. Either of these senarios would exclude 9 from being a solution to cells 1 and 5. This would leave these two cells (1 & 5) with just one possible solution - 1. Clearly this is a nonsense, as whichever of these cells you choose to put 1 in leaves the other cell with no possible solution. A similar situation occurs if you suppose 1 as the solution to either cell 8 or cell 9.
Therefore, you can remove both 1 and 9 as possibles value from cells 8 & 9. For this particular example this does not immediately solve a cell. However, you now have another exclusive pair (5,8) in cells 8 and 9 and this may lead to further eliminations in that region.