Dimensional analysis is a method used in chemistry, physics, and other sciences to convert measurements and to determine something's dimensions. Sometimes it is called factor label method or unit analysis.
Any math done with numbers must also be done with their unit labels. For example, when dividing 50 miles driven by 2 gallons of gas used, you not only divide 50 by 2 to get a result of 25, you also have to divide "miles" by "gallons", which gives the unit "miles/gallon" or "miles per gallon". The final answer is "25 miles per gallon".
Looking at the unit labels can help in deciding what to do with the numbers. For example, to convert 2.3 miles to some number of meters, use the equation "1609.34 meters equals one mile" or 1609.34 meters per mile. Using division, the unit labels will be miles/meters/mile, which ends up as miles2/meter, which is not just the meters. With multiplication, the unit labels will be miles × meters/mile. The miles will cancel, leaving just meters.