Q:

What does "First Class" refer to in X-Men: First Class?

I am confused and curious about the meaning of "First Class" in X-Men: First Class. What does it refer to?

A:

They're the "first class" of Xavier's school for gifted youngsters, as well as the "first class" of the X-Men.
With regards to the title being some sort of pun intended to denote the characters as "high quality", I'm going to argue that it's not and is simply intended to indicate they are the first class of both Charles' school and the X-Men.
From the section on the film's development on Wikipedia:

As producer Simon Kinberg read the comic series X-Men: First Class, he
  suggested studio 20th Century Fox to adapt it. Kinberg, however, did
  not want to follow the comic too much, as he felt "it was not fresh
  enough in terms of storytelling", considering them too similar to
  Twilight and John Hughes movies, and also because the producers wanted
  an adaptation that would introduce new characters. Both Kinberg and
  Shuler Donner said that they wanted characters with visuals and powers
  that had not been seen and that worked well as an ensemble, even if
  they did not work together in the comics. Shuler Donner later said
  that the original idea was to green-light First Class depending on the
  success of X-Men Origins: Magneto. That project was seeking
  approval to film in Washington, D.C., and by December 2008, Goyer said
  filming would begin if X-Men Origins: Wolverine was successful. The
  story was moved forward to 1962, and involves Xavier and Magneto
  battling a villain.

Given they're also referencing the previously intended Origins series of the X-Men franchise, this would further indicate that "first class" is merely intended to convey that the cast of characters involved are merely the first X-Men.
Additional research on the comic series X-Men: First Class mentioned in the excerpt would indicate that the comic follows the early adventures of the very first X-Men team.
As such, the title of the movie shares its name with the title of a short run comic series, which was designed to detail the exploits of the "first class" of the X-Men team. Any inference of the term "first class" to indicate a high level of quality would therefore seem to be either inaccurate, personal interpretation, or both, but certainly not an intended pun.

A:

It's a pun.
'First-class' as in 'excellent' or 'high quality', and "first class" as in they are the initial group of students.

