Arc welding is used for joining metals. The electrical arc reaches very high temperatures - in this case well above the boiling point of iron - so small droplets of the weld pod can be sprayed around rather like a miniature volcano. These glowing projectiles follow ballistic trajectories - parabolic arcs. The camera shutter was open for just th of a second so only short sections of the parabolas are recorded. Those drops near the bottom of the frame have cooled so rapidly that their trails start to vanish in mid-air.
*Warning: never look at an arc without proper eye protection (smoked glass or goggles).