Photographers and outdoor people enjoy it for it's mystical colors it can display. The colors are mostly produced by bounce light off of the clouds and atmosphere.
It is a very peaceful and magical time. In as little as an hour the world changes from day to night, or from night to day.
Have you ever just sat in the woods at twilight?
If the wind was blowing all day chances are now it will calm itself.
The animals that run around all day start to go and hide. The night time animals start to come out and make their appearance.
It's no longer day, and it's not quite night, it's somewhere in between. It's the magic hour.