When you add your gDNA to the PCR reaction mix, the volume of gDNA is generally much lower than the PCR reaction volume.
Also, when you pipet, you loose a certain percentage of your liquid sticking to the tip (let's say 5%).
Therefore, if you do NOT pipette up and down, you loose a certain percentage of the gDNA volume within the tip (5% of your gDNA - I use 4 ul). Let's assume there was 100 ng of gDNA per 4 ul, then you've just lost 5 ng of template.
(BTW you should never pipette less than 2 ul of gDNA anyway to achieve a high accuracy, dilute with H2O if neccessary)
If you do pipette up and down, you loose the same volume of liquid on the tip (since it is the tip/volume you used to pipette your gDNA with), but your gDNA is diluted with the PCR reaction (in my case 16 ul), thus the actual loss of gDNA on the tip is much lower (1ng as it is a 1:5 dilution).
Pipetting up and down is a standard pipetting technique that should be used whenever you are pipetting, not just to mix your reaction, but to reduce the loss of (undiluted) liquid that you are adding to another liquid. A quick vortex and then spinning down is another of those standard procedures that should be used when setting up reactions, except when pipetting materials that are sensitive to mechanical disruption (such as DNase or competent bacteria while transforming).
I hope this helps.