There isn't any canonical explanation yet, or at least it isn't made obvious by the movie.
It is heavily hinted that Darth Vader is Kylo Ren's role model, so it's no wonder that Kylo Ren wants to look like Vader.
He meditates next to Vader's mask.
When he tries to read Rey's mind and the telepathic connection he has established backfires, causing Rey to read his feelings, we learn that he fears he will never be as strong as Vader.
But it is also heavily hinted that Kylo Ren looks more intimidating, fearsome and powerful than he actually is.
He is not a skilled Force user. First, his roster of tricks is pretty limited. He can do Force telekinesis, Force telepathy and... that's about it. No Force throw, no Force jump, no saber throw, no Force lightning. Second, he fails both times he tries to use his powers on other Force-sensitive people. When he tried to read the map out of Rey's mind, it backfired on him and caused Rey to read his mind. When he tried to pull Luke's lightsaber out of the snow, it actually went to Rey.
At the end of the movie, Snoke says that Kylo Ren must "complete his training".
Kylo Ren's lightsaber has a very rough blade (see the official movie poster for comparison of Kylo Ren's lightsaber and Anakin Skywalker's one), hinting to a less-than-stellar build quality. By the way, it is canonically established by Star Wars Clone Wars season 5, episode 7 ("A Test of Strength") that building a lightsaber is a test of Force-wielding.
The Dark Side of the force provides "abilities some consider to be unnatural" (Palpatine in Revenge of the Sith) and excessive usage of these powers permanently changes the user's appearance. Now, when Kylo Ren takes off his mask for the first time, he looks... handsome? innocent? disappointing for a Darksider? Either way, he obviously isn't yet intimate with the Dark Side.
Finally, let us not forget that Kylo Ren is one of the Knights of Ren.
The movie doesn't really explore that part of the story. We know that Kylo Ren is one of the Knights of Ren, but we are never told about any other characters in the same group. It seems that current consensus among fans is that the Knights of Ren can be seen in the Force vision that Rey had when she touched Anakin's lightsaber. This is the best image I could find. As we can see, most of these people wear masks.
I am not sure about the guy with the spear, the second from right. I think we can see his eyes, nose and some facial structure that goes around his mouth (maybe coincidentally, but not unlike Sith race). But this might be a mask after all. Wookieepedia has another screenshot that leaves little doubt that the guy with the spear wears a mask, too.
So, maybe wearing a mask is just something that Knights of Ren do.