The Once and Future King comes from what was thought to be inscribed in Latin (fancy schmancy!) on Arthur's grave upon his death: Hic jacet Arthurus Rex quondam Rexque futurus (Here lies Arthur, the once and future King).
This means that Arthur was once the king, and will return to be king of England again at the time of the country's greatest need. It also ties in neatly with the time issue of Merlyn living backwards. Finally, in contrast with Malory's super-downer title Le Morte d'Arthur (The Death of Arthur), White's title doesn't necessarily focus on the fact that Arthur will die. It directs our attention to other aspect of his life—like his kingship.
The other titles are fairly self-explanatory, and either directly reference an event or figure in the text (The Sword in the Stone and The Ill-Made Knight), or use a metaphor for a character or a major concept in the text (The Queen of Air and Darkness and The Candle in the Wind).
Let's get to the easy ones first. The Sword in the Stone gets its title from the climax of the book: when Wart draws the kingship sword from the anvil and becomes Arthur, King of England. The Ill-Made Knight refers to Lancelot, who the spotlight shines upon mercilessly in this book (he's ugly and unfortunate—both meanings of "ill-made").
The Queen of Air and Darkness, of course, refers to Queen Morgause, although we don't learn that until the very end of the book. White lifts this moniker from an A.E. Housman poem in his grouping entitled "Last Poems".
Finally, The Candle in the Wind refers to Arthur's ideals that humans will be able to eventually vanquish Might and start a gentler, more peaceful civilization. He's protected these ideas like a candle, the flame of which he's shielded from the rough winds, and he's passing this flame on to the future generations (via Malory) to protect and nurture.