Not a meteorologist, but I did once write about this stuff for beer money.
A rising parcel of air enters regions of progressively lower pressure with altitude, and therefore expands. In expanding, it does work on the surrounding air and therefore cools. If it is unsaturated ("dry"), it cools at a characteristic rate, the dry adiabatic lapse rate, which is around 10°C/km. If it is saturated ("moist"), the cooling causes water condensation, which releases latent heat that offsets the cooling process. So there's also a moist adiabatic lapse rate which is less than the dry adiabatic lapse rate: typically about half.
So moist air cools half as quickly as it rises, and therefore retains a lower pressure, and therefore is more buoyant than dry air. We're therefore more likely to see strong convective instability when moist air rises, which accounts for those billowing towers that develop on top of cumulus clouds. More rising air draws in more air at ground level, and does more work aloft.

Grant Hutchison

Edit: I quite understand that you'd rather hear this from a meteorologist. Googling on "moist adiabatic lapse rate" (or "saturated adiabatic lapse rate") and "thunderstorm" will turn up any number of lecture notes and information pages prepared by meteorologists, which will (I hope!) say pretty much what I describe above.