What does it mean by a manga series being licensed, how does it affect online readers, and how can I continue reading it?
The Bleach manga is being published in Weekly Shōnen Jump, which belongs to Shueisha Inc. - a major Japanese publisher. 

In the case of MangaFox, Shueisha requested the removal of Bleach, Naruto and One Piece from the site (you can read more here), so I would assume something similar had happened to it as well. For the reference, the holder of the rights to publish Bleach in the USA belongs to Viz Media, which has also requested the removal of the series from some of the websites before.