There are several ideas, none of which exclude the other: [note that Louis and Marie Antoinette got married on May 16, 1770]

Louis may have had some sort of psychological issue with sex:

On 8 August Marie Antoinette urged her husband to confide in her. Louis assured her that he knew what was involved in marriage, but that he had imposed upon himself a temporary code of conduct, the term of which had expired, and that at Compiègne he would live with her in the greatest intimacy. But at Compiègne nothing changed. The dauphin continued “pausing for reflection” and the weeks passed in the same fashion. The king resigned himself to having to intervene, but the dauphin requested still more time to “overcome his fear.”

Similarly,

On 23 January 1771, new confidences by Louis to his wife: he confided in her that for the first time he was beginning to feel a certain fondness for her, and that on their wedding night he had intended to consummate their marriage, but that he was held back by a pang of fear that had grown inside him ever since; that he perceived nevertheless that friendship and trust were gaining the upper hand and that he had resolved to obtain for himself the joy of being intimate with her.

Louis may have had something wrong with his penis:

The idea that the dauphin might suffer from phimosis [NSFW] was not new. The previous year, Louis XV had asked his grandson Don Ferdinand -- another member of the family late to discharge his conjugal duties -- if he had not had to undergo a minor, quite common operation which his cousin (the dauphin) might also require. La Martinière examined the dauphin and put the king fully at rest.

This is from Count Aranda, 5 August 1774:

“Some say the frenum is so short that the prepuce [NSFW] does not retract upon entry, causing His Majesty much pain and forcing him to curtail the movements necessary to complete the act. Others think a tight prepuce prevents the head of the penis from being exposed, making it impossible for His Majesty to have full erections.”

Louis consulted with numerous doctors, though, and they did not seem to think he needed an operation. This is from the Queen in 1776 to her mother, referencing a doctor:

“He said pretty much the same thing as the others, that the operation was not necessary and that all would be well without it ...”

Or, (and this one is honestly hilarious, there's no getting around it) Louis may simply not have known what sex was. This is from Joseph II of Austria, the Queen's brother, whose 1777 visit seems to have catalyzed the consummation of the marriage:

“In the end, it’s not a weakness of the body or spirit; it’s simply that he hasn’t had his ‘let there be light’ moment yet, his technique is still in the process of formation ... In his marriage bed, he has strong erections, he inserts his member, remains there for perhaps two minutes without moving, withdraws without ejaculating, and while still erect, bids good night. It’s incomprehensible. He sometimes has nocturnal emissions but always while lying motionless. He’s satisfied, saying he does it only out of a sense of duty but has no desire for it. Ah, if only I could have been present once, I would have set him straight! He should be whipped until he discharges in anger like a donkey. My sister does not have the temperament for this and together they make an utterly inept couple.”

All quotes are from http://www.historyofcircumcision.net/index.php?option=content&task=view&id=78