The BMW logo has been very constant and consistent over the years. The largest change was the font from serif to sans-serif in the 50's. The BMW checkered pattern is thought to be representational of spinning propeller blades from when they built those.
the blue and white is also symbolic of the Bavarian flag, the origin of the company. In the 70's and 80's the motor sport logo had a lot more blue to represent water with the red ring that appears to be a boat bottom.
In 2000 BMW logo changed from the 1954 flat logo to a more beveled 3 dimensional logo to make it look more dynamic.