This is really a funny decision to read, the court was NOT amused with the petitioners' nonsense.
Basically, plainclothes officers in an unmarked car were out looking for shit to do in a high crime area. They saw a pickup truck which was stopped at a stop sign for a long time, which aroused their suspicions (Whren was the passenger in the truck). When they turned around and drove towards the truck, it suddenly sped off after turning without signalling. The plainclothes officers caught up to the truck (which had to stop with other traffic at a light), approached on foot, and identified themselves as officers. The justification given for the contact was to warn the driver of the truck for the traffic violations. When the police approached, they saw that both the driver and passenger had crack cocaine and they arrested them both.
Both were convicted, and appealed their conviction because even though the officers had PC for the traffic violations, they asserted that a reasonable officer wouldn't have stopped them under those cicumstances and that the traffic stop was actually a pretext for a criminal investigation. The court held that as long as the facts of the case objectively constitute probable cause, it doesn't matter what the officers subjective intent was. The convictions were upheld.