A retrograde orbit is an orbit where the satellite travels in an East to West direction instead of the common West to East orbit. The normal West to East orbits are known as prograde orbits.
Retrograde orbits are uncommon due to the much higher velocities necessary for successful launch and the associated higher costs. During a prograde launch, rotational velocity of the Earth is added to the velocity of the launch rocket. In a retrograde launch, the rotational velocity of the Earth is subtracted from the velocity of the launch rocket.
Satellites designed to observe the Earth are sometimes launched in sun-synchronous retrograde orbits in order to maintain a constant angle of surface illumination.
Satellites in retrograde orbits could theoretically be used as ballistic weapons to smash into satellites in prograde orbits.