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When there is fluid or pressure of any kind on the eardrum, dizziness occurs.

In fact there is a test using sensors on the head, called an electronystagmagram.
http://en.wikipedia.org/wiki/Electronystagmography
During this test, the eardrum is stimulated with heat or air blown into the ear canal...and the resultant electric impulses are recorded with electrodes. Dizziness failure with this stimulation then points to problems with the vestibular nerve.

When you blow your nose too hard, you are putting pressure from the inside of your ear on the eardrum in a similar way and the sensory nerves fire and cause dizziness.

This is sort of a warning to not be so strong in the maneuver and to do it more gently. Using a mucus dissolving drug like Mucinex and drinking more water daily can thin the mucus for you so you don't have to blow so hard. In extreme cases you may damage or rupture your eardrum.