A common way to get this look is a long exposure in a dark scene.

Typical setup:

• Use a slow shutter or Bulb mode.
• Include small light sources in the frame.
• Move the camera during the exposure—side to side, rotate it, move it forward/back, or zoom the lens—to turn those lights into streaks.
• Fire a flash briefly to freeze the main subject or room for an instant while the rest of the exposure records the moving light trails.

That combination explains why the scene can look relatively defined while the background lights smear into streaks.

Another possible method is light painting: keep the shutter open in a dark room and use a flashlight or other light source to draw streaks manually. Multiple exposures or a composite can also create a similar result, but the effect can absolutely be done in-camera with long exposure plus motion and/or flash.

To try it yourself, shoot in a dark room, stabilize exposure with a low ISO and small aperture, use a long shutter, then experiment with camera movement and a brief flash pop.