Trophies and Achievements are designed to enhance our gaming experience. That's the idea.
They represent specific challenges completed and those who love the feature will say a game's longevity greatly increases. You spend a ton of extra time enjoying the adventure in a variety of ways; many challenges are quite creative and even open up parts of the game you never really enjoyed before.
At the same time, there are those who just don't see the significance. Back in the old days, it was all about points. "High score" was a universal term and in the arcades, that's about all that mattered. Of course, everything is more complex these days; we're talking about interactive entertainment and it's almost an insult to call these products "video games." That means Uncharted 3: Drake's Deception and Pac-Man are technically in the same category, and even for the most ardent purist, that's tough to swallow. So we've moved way beyond "high score."
And yet, aren't Trophies and Achievements just a more elaborate way of keeping score? We count up the number we have and in truth, once they're achieved, it doesn't really matter to anyone what you had to do to get them. Those who don't appreciate this method of "keeping score" – which sort of implies that those who get a ton of these "awards" are bigger or better gamers than others – say that Trophies/Achievements are unnecessary. Worse, they might actually bring an even more unnecessary competitive angle to a game that doesn't need it. Maybe getting some obscure achievement alters our focus and drags us away from the core concepts of the game.
Then there's the whole need for edification thing. "You walked down a hallway…Trophy!" "You completed the tutorial…Trophy!" As if we need a shiny thing to make us feel better about our accomplishments, and then we can brag about how many of those shiny things we have. Do we really need this more complex version of keeping score? Or do you see it differently? Do you feel more satisfied when you hear that little "ding" and you see the notice? I'm just wondering how much this feature has altered how we approach our gaming entertainment.