Dimensional Analysis is a way to simplify complex calculations. This method is relatively easy to learn and master, and may seem like a waste of time to the advanced math and/or science brain. I've found it very useful. Especially for Chemistry, Physics or Electronics classes.
In short, Dimensional Analysis is a way of arranging values and their respective units in fractions or ratios. When two units are exactly alike and diagonaly oriented, they are 'crossed out' or eliminated. If, after all the crossing out you end up with the unit(s) desired, then you can simply multiply across and then divide.
Here is a small demonstration (ASCII for your pleasure) of Dimensional Analysis on a Stoichiometric problem:


N2 + 3H2 => 2NH3

             4.3gN2      1mol     3 mol H2   2.02g   0.93g of H2 
  ?g of H2=  ------- x -------- x -------- x ----- = -----------                 1       28.02g    1 molN2    1 mol       1

Thanks to Storm Damage and vivid for pointing out the pre tags! D'oh!