Karam was stopped by a Wyoming trooper for following too closely. During the traffic stop, the trooper told Karam he was going to give him a warning. The trooper also talked to Karam about his travel plans and whatnot while he was running his license through the computer (apparently Wyoming is one of those places where the drivers in traffic stops sit in the patrol with the cop. Crazy bastards). Karam said something early on about needing to use the bathroom, and the trooper pointed out that there was a truck stop which Karam had just passed. Karam said something which the trooper believed (possibly mistakenly) to mean that he had stopped there to buy tea, which the trooper knew to be false. Karam gave vague, inconsistent responses about where he was going and where he had stayed, and claimed to have flown from Akron to LA and decided to rent a car to drive back to Arkon. Karam's car apparently contained some cardboard boxes which the trooper thought were suspicious because he was aware of another case where marijuana had been packaged in similar boxes. Other than that, it contained less luggage than the trooper would have expected for the trip. Karam was given a warning for the traffic violation, released, and then asked for consent to search his car. He refused.
Then the trooper told him he was not free to leave, and detained him while they waited for a K9 to arrive and sniff the car. The dog alerted, the car was searched, the drugs were found, Karam was arrested and eventually convicted. He appealed, and the US Supreme Court affirmed his conviction.
The court explained that investigative detentions must be justified at their inception, and reasonably related in scope to the circumstances that justify the stop. Traffic stops are similar to investigative detentions, so the same applies to them (they can last long enough to check records, fill out tickets/warnings, etc). During the stop, an officer is allowed to ask questions both related and unrelated to the reason for the stop, so long as unrelated matters don't prolong the stop. Once the business of the stop has been handled, an officer may continue the stop only if the officer develops additional reasonable suspicion for continuing the stop or if the stop becomes consensual (I've always thought downgrading from a compulsory stop to a consensual one is a stretch, but so far no one has screwed that up badly enough for the courts to drop the hammer).
In this particular case, the court discounted some of the factors that the state courts had relied on for determining that there was PC. Even though reasonable suspicion can be based on factors which have innocent explanations, the court is only willing to give us just so much leeway with that. The court held that there was nothing suspicious about a stack of cardboard boxes in a car, The court also held that even though LA apparently exports drugs and Akron apparently imports them, there is nothing suspicious about driving from one metropolitan area to another (even if you flew the other way a week and a half ago).
The court noted that Karam may not have actually claimed to have stopped at the truck stop, but that the trooper understood him to have claimed that. Reasonable suspicion must be based on facts known to the officer at the inception of the stop, but it can also be based on facts which an officer mistakenly believes to be true so long as the mistake of fact is reasonable. So even if Karam didn't actually say that he stopped, if the trooper thought he heard that then this perceived lie can be considered in determining whether or not there was reasonable suspicion.
Other than that, there was the inconsistent responses about travel arrangements. The court held that although none of the facts relied on in this case would alone constitute reasonable suspicion, reasonable suspicion is not a "divide-and-conquer" analysis; the situation has to be taken as a whole. The various facts of the case viewed together were sufficient to justify detaining Karam until the drug dog showed up.