I have always been a sci-fi fan ever since I was about 5 years old. I was a child of ten when Star Trek premiered and I loved it. When I was a teen it ran in syndication and every day when I got home from school I watched Star Trek. I came to love not only the science fiction in the stories but the characters themselves. This love and enjoyment found a place when TNG, DS9, VOY and ENT were running as well, and it was the characters that made me love these incarnations. I especially grew to love and enjoy TNG and DS9.
The Star Trek universe and philosophy has also been part of the appeal and without new shows to watch books can be an excellent way to enter into that universe and experience new adventures with your favorite characters.
I also enjoy reading Star Trek books because it's very easy to pick up a book where you already know the characters. I don't have to keep notes in my head, and sometimes on paper, to keep track of who's who and what's what. Now there are always new characters introduced in every book but the crux of any Star Trek book usually revolves around characters you already know and love.
I could go on but those are the main reasons and not to mention that many of them are pretty good stories in their own right.