If you live anywhere near a coastline and the Tropics, you are probably pretty familiar with the various annual atmospheric bitch-slaps that Mother Nature sends your way: things like hurricanes, cyclones, tropical storms, tropical depressions, the sorts of things that remind you that the best laid schemes of mice and men go often askew (especially regarding building construction and evacuation routes).
It's really simple, how it works: whenever the sea warms up past a certain point, it starts generating storms. The degree to which the sea warms up, and especially the differential between the water temperature and the air temperature, makes a huge difference between a rainy day at the beach and a Category 5 leveler of cities. I won't belabor the point, because there're already a lot of good nodes on the various flavors of tropical cyclone that come around every year.
But when the seas warm up past about 50°C (122°F), you get storms that make Andrew and Katrina look like mere farts in comparison. These mothers of all storms are called 'hypercanes'. Thankfully, the seas never warm up past about 35°C under normal circumstances, and thankfully, a significant enough departure from 'normal circumstances' probably hasn't happened for about 65 million years, when the Yucatán and its surrounding seas served to convert about 400 sextilion joules of kinetic energy into thermal energy.
The heating caused by the impact boiled the seas and the superheated water vapor rose, only condensing when it hit the stratosphere about 30km up (20mi). Think of your usual cycle of hurricane formation, only much, much worse. Computer simulations suggest that wind velocities could have edged into the lower end of the transsonic range; estimates tend to be around 800kph (500mph). To compare, the highest recorded wind velocities for a hurricane were around 300kph (190mph). That's one bad muvva of a storm.
About the only thing that people agree on about hypercanes is their incredible 'Aeolus just had lunch at Taco Bell' wind velocities. Some scientists think that the hypercane that formed during the K-T extinction event could have spanned the entire North American continent, from Alaska to Florida. The eye could have been as much as 300km (190mi) across, and the storm could have kept pounding away for weeks, depending on how slowly the water cooled. Others think of hypercanes as more akin to methed-up tornados, about 15km (10mi) across, but by no means less destructive to anything unlucky enough to be caught anywhere near the beast.
However broad these storms may have been, it's their height that gives them their potential to contribute to mass extinctions; they stretch twice as high as a typical hurricane, sending a massive gout of dust and water vapor into the stratosphere (where things like that tend to linger a bit longer than in the troposphere thanks to the prevailing winds). The debris thrown up would have altered the climate very suddenly and anything that couldn't adapt would perish. Combine that with the very obvious effects that a massive asteroid impact would have had on the climate, and you have a recipe for a very rough couple of millennia as the biosphere struggles to recover.