Something that's meteorological is related to the weather or changes in the Earth's atmosphere. If you're interested in a meteorological career, it means you'd like to be a meteorologist — a weather expert.
Meteorological events include things like fog, rain, tornadoes, and hurricanes. They are all caused by meteorological changes and shifts: in the temperature, air pressure, and amount of water vapor in the atmosphere. The word meteorological comes from the Greek root meteorologia, "discussion of high things," from meteor-, "thing high up," and logia, "the study of."