Achievements codify what is significant by some objective standard. Sure there are really easy achievements that no one cares about, and hard as nails achievements that require the sacrifice of livestock to have any hope at getting, but that has little to do with the general gratifying nature of achievements.
Think about it this way: Games used to have high scores (some do, but people stopped caring about scores anyways). It was a way to rank individuals who played them according to their success. This is a more egalitarian way of developers saying to players "This is what deserves praise. If you get this far, give yourself a pat on the back."
It also universalizes alternate playing styles in many ways. By having an achievement for a task, it lets all gamers know that that task is a legitimate way of playing the game. Rather than someone setting the personal goal of exploring all of Azeroth and their guildmates saying 'oh, that's nice', the game announces to guildmates that it's done, and I'm willing to bet it's usually met with compliments or praise. Instead of just saying 'I'm going to throw urine on that guy I've been dominating all match' and it just being funny, it's also a challenge that many people try because it's an achievement.
Many people who wouldn't have engaged with alternate ways of playing games diversify their play because achievements are there to say 'this is a challenge, are you up to it?"
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