The big bang theory, to answer your second question first, is a theory that assumes that the whole universe, all energy and matter in it, started as a condensed, enormously hot and dense, point like state 13.7 billion years ago. That means that at this point, all the stars, galaxies, planets, everything was condensed into one single point. From then on, after the "big bang" which can be thought of as a gigantic explosion, the universe has been expanding, with the galaxies that came into existence moving away from each other. Evidence for this fact has been observed and is one of the experiments supporting the big bang theory, as opposed to a theory of the universe which assumes that the universe has simply always been there. Which is an answer to your question "why scientists believe this happened"? Another important piece of evidence in favor of the big bang theory is the cosmic microwave background radiation, which is not so easy to explain, but may be thought of as a remainder of the flash of light coinciding with the "explosion" of the big bang. The continuous expansion of the universe is what allows us to still "see" this remainder.
So the result of the big bang would be the coming into existence of the universe as we know it, not just our galaxy but all others, as well. What exactly happened DURING the big bang is obviously not easy to investigate, and more a matter of theory than experiment. This is easy to understand if you liken the big bang to an explosion - it's hard to say what exactly happened at the point of the explosion right as it was happening, or rather to relate what was happening to something familiar.
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