The subject is in complete darkness, so a long exposure (1 or 2 seconds) combined with a bit of camera wobble makes the lights in the picture leave trails like that but you don't get a blurry subject.

Combine that with a camera flash (1/1000s maybe?) which illuminates the subject and there you have it. (the flash also dimly illuminates the objects in the bottom-right of the picture).

Edit - the flash will either fire at the start or at the end of the exposure, controlled by the first/second curtain sync setting. I don't think it would matter too much for this exposure, but for an effect like car light trails appearing to streak away BEHIND the car (Car light trails, Google images), you'd use second curtain. so with the shutter open for a second or two you capture the light trails, and then the flash fires as the shutter close (2nd curtain) to illuminate the car, frozen in the frame with the light trails behind it.

Default for curtain sync is usually first, which would illuminate the car as the shutter opens and THEN capture the light trails, which would then appear to streak AHEAD of the car.