Original: The operator of Heathrow, BAA, claims that Heathrow is the "world's busiest international airport", but it is only the world's third-busiest by total passenger traffic, after Atlanta-Hartsfield-Jackson and Chicago O'Hare, which are also international airports.
Simplified: Heathrow is also Europe's busiest airport for passenger traffic, and handles more international passenger traffic than any other airport in the world.