This technique is used when a high degree of dilution is required.
For example, you may need to dilute a solution by a factor of one million. This would be quite difficult to do in one go. You could start with 1 cm3, but if you dilute this by a million you would end up with 1,000,000 cm3 of solution. This is 1000 litres, or a lot of solution! Alternatively if you wanted to end up with a litre of solution, you would need to start with 0.001 cm3 of original solution. This is very small and would be difficult to measure out accurately.
The solution to the problem is to use serial dilution. We start by taking 1 cm3 of original solution and dilute it to 100 cm3 in a volumetric flask. This is now 100 times more dilute. We now take 1 cm3 of this diluted solution and dilute it to 100 cm3 in a volumetric flask. This is diluted by a further 100 times. Finally we take 1 cm3 of the twice diluted solution and dilute it to 100 cm3 in a volumetric flask. Our total dilution is 100 × 100 × 100 = 1,000,000. An alternative would have been to do two 1 cm3 to 1000cm3 dilutions - 1000 × 1000 = 1,000,000.