Earlier quoted context omitted.
The difference is generally that higher-paying (i.e. first and business class) passengers get seated first (because having your higher-paying passengers wait for the lower-paying passengers is undesirable), and they're also generally seated at the front of the plane so they don't have to wait when getting off either.
Though back-to-front means that the expensive passengers can arrive closer to the departure time, and don't have to suffer through everyone in economy shuffling by them and hitting them with their carry-on. It does cost them some flexibility, in that they can't board as soon as they arrive. But my experience is that sitting outside of a plane is generally far nicer than sitting in first class... at least on domestic…
If you boarded last, you'd get no pre-takeoff beverage to sooth your nerves.
At some airports, they board the larger jets through multiple doors - First/Business gets their own, and everybody else crams into the other one. I've also been asked to wait to board while the first class gets situated and has their pre-flight drink. (I've also had that pre-flight drink, and it's pretty nice!).