The weather creating the conditions is atmospheric convection from a combination of the sun heating the ground (unevenly) and instability of the atmosphere in between the ground and 5-10,000 feet.
The instability occurs when the lapse rate (temperature drop with altitude) is steep, so that if a package of air is warmed at the ground and something gets it moving up, it wants to go higher faster, the higher it goes. More or less like a hot air balloon.
So you end up with a vertical circulation in the atmosphere between the ground and cloud base. Air rising, and beside it, air falling.
The vertically rising columns of air are called Thermals. If the humidity of the air is high enough, cumulus clouds form at the top of the thermal as the air cools to the dew point at 5, 7, or 10000 feet or wherever.
Gliders exploit this vertical circulation to remain airborne. For power pilots, it causes an unpleasant ride as you constantly fly through air that is rising, then air that is falling to fill in for the air that was rising.
Anyway, they called you before because the weather conditions were rough, due to that kind of thermal activity, and they knew there was a high risk you'd get airsick, which is bad for intro flights, as you can imagine. They were playing it safe for a potential long term customer.
It'll be worst between 11 am and about 4 pm and if your flight was say, scheduled for 1 pm, and the required conditions are present, the chances are really high it'll be too rough. If the winds are high, it breaks up the thermals and makes the ride even choppier, so worse still. I would never take anybody new flying on an afternoon with lots of convection and especially convection + high winds. They'd be barfing within 20 minutes.
Next time you book your flight, try to book it for early morning, say 8 or 9 am, when the air will be silky smooth even if it's going to be a convective day. Or, evening, say after 5 pm.
At some point later you'll find out if you have a problem with air sickness in the bumps. Generally even if you do get sick, repeated exposure desensitizes you and the airsick problem goes away. If it is a problem, spending some time on a park swing can help with the desensitization. It's basically a variation on seasickness.