The Épine Dorsale (French for "dorsal spine" if taken literally, "backbone" for the rest of us) is a somewhat loosely used term in chess. It refers to a particular position a few moves into the opening that can lead to a great number of games. The widest interpretation of it is "the position arising from 1. e4 e5". Some sources give it as 1. e4 e5 2. Nf3 Nc6 3. Bc4, but this seems to me to be incorrect since Bc4 introduces the Giuoco Piano or Italian game which has been known by that name for a very long time.
In any case the most common (and in my opinion the most sensible) definition of it is "the position after 1. e4 e5 2. Nf3 Nc6". This is a very classical sequence of opening moves indeed, and for many players it is a standard to be bashed out at the beginning of any game. It can lead to all kinds of things, most notably the Ruy Lopez (Spanish game), the Giuoco Piano (Italian game), the Scotch game and many, many flavours and continuations of these. Most openings most people will have heard of stem from this position. Four knights, Vienna game, Halloween... you name it, chances are you get to it from here.
This is not to say all chess games begin with it. The Sicilian is probably the most popular one out there (at least at the higher levels of players) and it starts with 1. e4 c5.