This one I can answer correctly! Haha
Some of the lyrics that confuse you use idiomatic expressions.
"The time of our lives" is an expression that refers to the best part of your life. Many people say college was the time of their lives. Adele is saying it feels like just yesterday everything was perfect.
"To show up out of the blue" means to appear without warning. If a friend stops by "out of the blue", it means they didn't call or tell you they were coming. It can be used in a positive sense or in a negative sense. "And then, out of the blue, I won the lottery!" "Everything was fine until a car came out of the blue and hit me."
"We were born and raised in a summery haze" is just a nice-sounding phrase that doesn't really mean anything, and the same is true of "bound by the surprise of our glory days," though "Glory days" is similar in meaning to "The time of our lives." There's a wonderful song by Bruce Springsteen called "Glory Days" that is all about the characters in the song remembering when they were young.