If you're asking how that's done, that's a flash technique with a slow shutter sync. Most cameras will have a slow sync option in their flash modes, and most external flashes are compatible with this as well. Most DSLRs will allow you to choose front or rear curtain flash, which determines when the flash will fire - at the beginning of the slow shutter or the end.
Essentially, the camera is metering and using a slower shutter speed as it would need to without a flash - in a dark environment, say a 1-second shutter, which would cause blur and light streaking with any movement. Sometime during that exposure, the flash is going to fire a normal flash (like 1/60 or 1/125) - either right at the beginning of the exposure, or right at the end of the exposure. The flash illumination will freeze any motion or action in the shot, but since the camera exposes for a longer period of time, any highlights or bright areas continue to pick up on the sensor, and will streak if you move. The photographer controls how much streaking, and the direction of the streak, by moving the camera in the desired direction and amount during the exposure.
Hope that helps.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses