Reading when it's very sunny out can be damaging to your eyes especially if you do not wear sunglasses when reading in the sun.
However I've read books and magazines etc in the sunlight for years and my eyes have never been harmed although if the sun does get too bright I do put on a pair of sunglasses to protect my eyes but it's not only for reading.
I wear sunglasses on very bright days to protect my eyes anyway and it makes the book easier for me to read too.
Reading books in the dark or poor lighting can also damage eyes so if your room is dark or has poor lightning it's best to use a reading lamp to help illuminate the book you're reading.