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I was watching documentary about Earth's formation National Geographic. They made this following statement.

......An astonishing event is about to take place.The Earth is on a collision course with another planet and about to experience the biggest bang in its history. The only reason we knew about this collision is because of the moon encircling the earth...

Then it went on, not clearly stating how the moon and the collision are related. Are there any studies done about this assertion?

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This is known as the Giant Impact Hypothesis or the "Big Splash".

As remarkable as it sounds, it is actually is the scientific consensus of how the moon was formed.

The Moon is generally believed to have formed from debris ejected by a large off-centre collision with the early Earth.

More evidence for this event, including: Earth's spin, the Moon's orbit, the Moon's core, lunar rock samples, and evidence of other collisions is listed on the Wikipedia page. It also describes the process. (I am comfortable relying on Wikipedia, because this is high-school-level astronomy.)

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As an aside: The Wikipedia page explains how the moon formed from the debris in a relatively quick period (between a month to a century). I once heard it took about 70 years (from a Skeptics Guide to the Universe podcast, so not a peer-reviewed source). Imagine living on Earth back then, and having your grandparents say "Ah, the moon isn't like it was when I was a kid. It's all in a single lump these days. It used to be spread across the sky..." – Oddthinking♦ May 12 '12 at 8:17

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