In Guardians of the Galaxy, after they defeat Ronan, Peter returns to his ship and opens the letter from his mother. Now we obviously knew that he read it before, since she mentioned the word "Star-Lord" in it, but the gift from her definitely still had ribbons on it. Why did he wait 26 years before he opened Awesome Mix Vol. 2?
Now we obviously knew that he read it before, since she mentioned the word "Star-Lord" in it,
Given Peter's (still secret) parentage, it's likely that "Star-Lord" was her nickname for Peter while he was growing up.
As for why he never opened the gift, this is never 100% explained within the movie or any bonus materials (that I'm aware of as of yet), but it makes sense thematically.
When we meet Peter, he's listening to Awesome Mix Volume 1 - likely given to him by his mother when she was still healthy. Peter's mom gives him the gift telling him, "You open it when I'm gone." As she is dying, he not only refuses to hold her hand, he actually runs out from the entire building. He refuses to accept that she's dead. From here on out, he continues listening to Awesome Mix Volume 1 - his connection not only to his mother but of Earth and not being alone. When Peter is explaining his walkman to Gamora, the subject of his mother comes up, and Peter is unable to say, or admit out loud, that she is dead.
By the end of the movie, Peter has become a very different person. In fact, all of the Guardians have. They've all grown from looking out only for themselves, and learned not only to look at the bigger picture, but to value friendships and relationships. They've given up only looking out for themselves, as they've learned that there are others out there that care about them and that they care about.
During the battle with Ronan, Gamora says, "Peter, take my hand!", echoing his mother's words. As Peter turns to look at Gamora, he sees his mother.
Now, Peter isn't afraid of being alone because he knows he's not. He can finally accept his mother's death and look towards the future. It's finally time to open the gift.
Because it's the last gift he's ever going to get from her, and to open it up is akin to accepting that and saying goodbye. He can only open it for the first time once.
During the course of the film, he makes new friends and goes through things that make the Universe seem more important. One might say that Quill grows up during the course of Guardians. To finalise that transition, he needs to finally let go of the painful end of his childhood on Earth.