They produce spores that are spread by the air. This occurs most commonly in the spring and warmer months and again in the fall. Plants produce pollens when they pollinate. Many plants spread their pollen by the air. One rule of thumb is that the plants with bright flowers tend to pollinate by insects whereas plants that are much more plain use the air to spread their pollen.
Insects pollinate roses, but ragweed is pollinated through the air.
Many people will develop their allergies by the time they reach young adulthood. While traveling in Australia I experienced for the first time in my life an asthma attack. That was last year in April when I was 59 years old. A week ago while visiting Washington, DC, I caught a cold and after a couple of days had another asthma attack. In both cases my symptoms were relieved by the use of an inhalant prescribed for asthmatics.