This song is basically a romantic song. It's about how Belle and the Beast were unfriendly to each other and were even a little scared of each other, but soon they began to fall in love with each other, and you can start to see that as this song is being sung. For example, as they are dancing Belle rests her head on the Beast's chest and he gets really excited.
I think this song also illustrates that looks can be deceiving. From the outside, the Beast looks like a hideous monster who is angry and selfish, but once Belle gets to know him, she sees that he is actually kind, caring, and even a little shy sometimes. It's teaching the lesson "Beauty shines within."