The Shining takes its name from the special power that Danny has for seeing things that other people can't and for communicating without using his mouth. Mr. Hallorann is the actual person who puts a name to this power, as he tells Danny,
"I can remember when I was a little boy, my grandmother and I could hold conversations entirely without ever opening our mouths. She called it shining."
This power of Danny's turns out to be crucial to the movie, since it's what allows him to call Mr. Hallorann for help when his dad goes nuts. Now it's true that Hallorann can't save Danny, but he does bring the snowcat machine that allows Wendy and Danny to get away from the Overlook Hotel.
It's interesting that Stephen King and Stanley Kubrick decided to go with The Shining as their titles, since this secret power of Danny's isn't necessarily the most important detail of the whole movie. After all, there's a ton of supernatural stuff in the movie that has nothing to do with Danny's power—creepy twin girls, elevators full of blood, a decomposing woman in the bathtub. (All of those would make excellent movie titles, in our humble opinion.)
But naming the movie after this does help establish Danny as the true protagonist instead of Jack Torrance, and this is something that we might need to be reminded of as the movie spends more and more attention on Jack.