I had the pleasure of seeing The Police live last year on their reunion world tour and was blown away. They have a such an amazingly distinctive and powerful sound for only a three piece! This groove comes from 1979's Reggatta De Blanc and Stewart Copeland's drum part is, as always, clever and unique. This groove is essentially a modified reggae 'one drop'. It sits perfectly with Sting's bass line and gives the tune a fantastic pulse.
Below is a nice variation Copeland plays during the intro to the tune, where the cross stick on beat 3 is omitted.