Street Light Pillars seen near Valley City, North Dakota on Febrary 24, 1979. Note the clear sky with star trails visible. Yet enough ice crystals were present in the zero degree air to create light pillars above each streetlight in the town.
This phenomenon generally occurs in cold (below 10-15 F) moist weather with very light snow that is really in the form of individual platelike ice crystals. The sky may be cloudy or clear enough for stars to show through. The pillars extend up and down in the vertical line passing through bright artificial light sources. They are similar to sun and moon pillars in that the light is reflecting off of the platelike crystals having different random orientations.
Street light pillars can be mistaken for the aurora borealis, a very different phenomenon. Street light pillars usually occur within 20 degrees or so of the horizon, aurorae can be higher.
More info may be found in the book "The Nature of Light and Colour in the Open Air" by A. A. Minnaert.