Here is the full sentence for the first one: Using the money they had received from the PayPal buyout, Chen and Hurley decided to create YouTube, to make uploading and sharing videos online as easy as anyone could want. It was the birth of a revolution.
Most words in the language originated as metaphors, including language, originate and metaphor.
The birth of a revolution IS a metaphor but, like all metaphors involving birth, death, rise, fall and so on, it is now so commonplace that it has lost any power or magic it may have had and no longer sounds like one.
It was a metaphor comparing birth to beginning, so literally it was the beginning of a revolution.