According to Nasa.gov, Hurricane Katrina formed after the warm rising air in the tropics formed into a cyclone. The hurricane began in the central Bahamas and came ashore as a Category 1 storm in southern Florida. After causing 11 deaths in that state, the storm made a southwestern turn and cut through the warm waters of the Gulf of Mexico.
The storm was able to intensify significantly through this prolonged exposure to the warm waters of the gulf. After spending almost three days gaining wind speed and size, Katrina made landfall in New Orleans, LA as a powerful Category 5 hurricane. This is the largest and most destructive category of hurricane, with sustained wind speeds of over 130 miles per hour and a storm surge of more than 5.5 meters above normal sea level.
The weather system that would eventually become the named hurricane initially formed in the southern Atlantic ocean and did minor damage in Brazil as an uncategorized storm. It was one of the first hurricanes to ever hit Brazil and the first to be spotted in the south Atlantic. Brazilian meteorologists didn't classify the storm as a hurricane as the wind speeds at that time were only 50 to 60 miles per hour.