I have never been more thrilled to have taken Astronomy in college! This question is right up my alley! The Great Red spot is essentially a weather storm on the planet Jupiter. It is formed by the rotation of gases in Jupiter's atmosphere. These gases are pulled into giant whirling vortex's, the largest of which is Jupiter's Great Red Spot. As such, this spot is a VERY defining aspect of Jupiter that can be seen even with a very low level intensity telescope. (It is a pleasure to look at it, I assure you!)
The climate conditions are responsible for the way in which the storms form. Gases are emitted from the core, extremely hot gases. These gases then begin circling or whirling the planet creating many storms.
The Great Red Spot is a storm that has existed for many years and pulls other smaller storms into it's rotation, thereby, increasing and continuing the enormous Great Red Spot.
Because Jupiter is such a large planet, the conditions in the atmosphere vary widely. There are extremely cold and extremely hot areas in the atmosphere. Weather conditions are mostly determined by hot masses of air in the atmosphere. The way in which the core of Jupiter's heat mass meets with lower temperatures creates the extreme weather conditions in Jupiter's atmosphere. The Great Red Spot is suspected to have lasted at least 150 years. The type of storm that makes up the Great Red Spot is cyclonic.
Just a tiny personal story for my conclusion. I remember looking through the university telescopes and being incredibly disappointed that the red spot was rotated AWAY from us at that point. I believe I made a sound similar to, "Ttthhhhppptttt."