basically, a blog widget is a kind of application to be added at a blog's sidebar.
i imagine it to be something that shows all the mangas in your list, the chapters that have been read/newest chapters etc.
by having it in blogs, it gives bloggers the benefit of showing readers how much they love reading manga
plus it's an additional promotion for allmangasreader (the size of the blogosphere is very big u know 
)some legal issues might b involved though (copyrights and stuffs) so dis is jz a suggestion. feel free to investigate further abt dis ^.^