It is a really interesting question! For me, I got into astrophotography after a number of years of visual astronomy and while I was studying astrophysics. I've always enjoyed photography and this seemed like the perfect match of interests, astronomy and photography.
I enjoy being able to photograph the sky and see things that I wouldn't be able to see otherwise, this is the point that Lewis was getting at. Being very technical minded I enjoy that technical aspect which is a part of the reason I enjoy mosaics; being able to photography entire areas at high resolution for later enjoyment.
Then there is the physics background where it is about trying to understand what has happened in the past in any particular region. A big part of my Masters was studying globular clusters and their evolution and that is something that I would like to, at some stage in the future, be able to research more through astrophotography.
As Suavi also mentions, it is nice to have a community to share the hard work with
