The above images are examples of a rolling shutter artifact. A "rolling shutter" means that the image is recorded one row (or column in portrait orientation) at a time, and not simultaneously. This means if the flash is of very short duration, it will only illuminate some pixel columns of the image. Here's what's going on in the first image:

This can be replicated with a flash set to strobe, and taking lots of photos with an iPhone 5, until one happens to contain the flash (you can also use video, or burst mode). Moving the flash so it's not illuminating an object (like this chair) will demonstrate the effect of the "beam" being "behind" things.

I used a Canon 550EX, set to "Multi" 1/128 and 30hz, and triggered manually with the pilot button.

Just holding the flash in front of the camera created a variety of images like:

It looks like the flash is not actually working, however you have to remember that for most of the frame, it's actually off. The only time the flash is on is during the white bar.

In my image the flash gives a white light (as a camera flash is obviously intended to), but lightning often shows up as a purple or pink tinge:

This is a surprisingly rare artifact, as it requires a brief lightning bolt to occur either entirely in the reset or read-out portion of the exposure, both of which are very short. To duplicate it I had to use a high speed strobe in sunlight to get the flash at the right time

Typical lightning photography with a rolling shutter looks more like half the image being lit by lightning, rather than the column we see above. Here's a more typical lighting shot at night with this problem:
http://www.productionapprentice.com/tutorials/ccd-vs-cmos/

Notice it's horizontal. The image is scanned one row at a time, but when you take a photo in portrait mode, then those rows are the columns.

Here I've repeated the flash experiment in a darker setting, and we get the half-illuminated image:

This video demonstrates what is going on with a rolling shutter, although it's a little misleading as it assumes the reset and read-out phases are happening simultaneously.

https://youtu.be/CwUE_4rKiO0

Update Aug 15 2015, a new example:

Here the illusion of it being a beam behind the clouds is particularly striking, as a band of dark clouds is partially obscuring the illuminated clouds behind. You can see part of the lightning bolt just below the power lines. Remember it's not actually a beam of light, it's just a slice of a scene as it would look illuminated by lightening.

The fact that the "beam" can go "behind" the clouds can seem confusing. But it's really just that the lightning is behind the clouds, and they are thick enough to block the light. I simulated a similar effect using the flash and a foam pool toy. If the flash is in front of the toy then it illuminates it, and you get the stripe across the toy. If the flash is moved behind the toy, then the toy is not illuminated, so the "beam" (the stripe of the image) looks like it's going behind the toy.

https://youtu.be/tCYApvOWo5M

This can be especially confusing when you notice the reflection of the "beam" on the hood of the car. Your brain naturally interpret this as a reflection of the scene, and so you think there's actually a beam in the sky. But if you look closely, you'll see the reflection in the hood is actually of a slightly different are of the sky. The "reflection" lines up perfectly vertically, whereas the nearby traffic signals are sloped. If this actually was a reflection of a beam in the sky, then it would also be sloped.

So while it's a reflection of sky illuminated by lighting, it's not the same area of the sky. It's a little unintuitive.

So again, what we are seeing here is essentially one normal image overlaid with a slice of another image that's illuminate by lighting. (And note that what looks like the reflection of a building in the lower right is actually the reflection of the air conditioning vent inside the car)

For more information please visit this perfect site

https://www.metabunk.org/solved-strange-beam-of-light-over-
mayan-temple-and-florida-lightning-rolling-shutter-artifact.t3244/

With a very special thanks to Mike West who explained us the complete mystery.

SECOND EXPLANATION

Light pillar

Wikipedia

A light pillar is an atmospheric optical phenomenon in the form of a vertical column of light which appears to extend above and/or below a light source. The effect, sometimes also called the crystal beam phenomenon,[citation needed] is created by the reflection of light from numerous tiny ice crystals suspended in the atmosphere or clouds. The light can come from the Sun (usually when it is near or even below the horizon) in which case the phenomenon is called a sun pillar or solar pillar. It can also come from the Moon or from terrestrial sources such as streetlights.

Formation

Since they are caused by the interaction of light with ice crystals, light pillars belong to the family of halos. The crystals responsible for light pillars usually consist of flat, hexagonal plates, which tend to orient themselves more or less horizontally as they fall through the air. Their collective surfaces act as a giant mirror, which reflects the light source upwards and/or downwards into a virtual image. As the crystals are disturbed by turbulence, the angle of their surfaces deviates some degrees from the horizontal orientation, causing the reflection (i.e. the light pillar) to become elongated into a column. The larger the crystals, the more pronounced this effect becomes. More rarely, column-shaped crystals can cause light pillars as well.

Unlike a light beam, a light pillar is not physically located above or below the light source. Its appearance of a vertical column is an optical illusion, resulting from the collective reflection off the ice crystals, only those of which that appear to lie in a vertical line direct the light rays towards the observer (similar to the reflection of a light source in a body of water).

Trivia

Light pillars have been known to produce UFO reports. Niagara Falls is one such area, where the mist from the Niagara Falls causes the phenomenon to appear frequently during the winter months, where the ice crystals interact with the city's many upward facing spotlights to create prominent light pillars.

https://en.wikipedia.org/wiki/Light_pillar