While the movie stays true to the storyline of the 1991 Disney movie, there were a number of things that were changed in the 2017 version. After all, the movie clocks in at 129 minutes - compared to 84 minutes in the 1991 version - so where do the extra 45 minutes come from?
First of all, there is a lot of backstory added to the plot. The Beast's story is given more substance by allowing glimpses into his old life. It mentions a dying mother, a father who corrupted the young boy's morale, and the fact that the people who should know about the castle in fact do not because they, too, are under the spell of the enchantress. But the Beast isn't the only one who has had an upgrade to his past. Belle's story was enhanced by telling the story of her mother, whom Maurice had to leave behind in Paris as she was suffering from the plague. In a later scene in the movie, the Beast takes Belle to her childhood home where she can see for herself what happened.
Another change occured in the number of songs used in the movie. New songs, such as the Aria, How Does a Moment Last Forever?, Days in the Sun, and Evermore were added in the 2017 version. Changes also occurred within songs, however, as we can see in Gaston. The lyrics were adjusted and shortened, while a dance sequence was added.
In terms of characters, the Enchantress is only seen in pictures in the prologue of the original, but in the new version, the Enchantress appears as the character Agathe throughout the entire movie, and at the end, she is the one to reverse the curse even after the last petal has fallen when she witnesses Belle's love for the Beast.
Many minor alterations were made, as well. For example, each time a petal falls from the rose, parts of the castle fall apart, and the staff appears less human. Those smaller changes occur mostly for added coherence, or to make the plot seem more plausible. In the 2017 version, the Beast is a well-read prince with an, as he says, expensive education. Their common interest in reading brings the Beast and Belle together. In the new movie, Belle is also the inventor, rather than her father, who is shown as an artist. Gaston is also given a little more backstory and character, and his buddy LeFou is given a larger role, as well.
Finally, jokes! There are some great, humorous lines in the new version that weren't there in the animated classic. Granted, some iconic lines were not used, but the new jokes (which I won't spoil!) do make up for it.