Book Bridge is an add-on for D5's core book module which serves to bring some of the functionality of D6 book module to D5. It should not be necessary in D6.
Specifically Book Bridge keeps track of which book a book node belongs to, enabling such features as views integration to filter for nodes within a particular book. It currently includes token integration which can allow for pathauto setups such as BOOKNAME/TITLE and a views argument for the book ID which can allow per-book searching.
Be sure to run update.php after installing Book Bridge in order to index any existing book nodes.
Alternatively consider trying Outline module which is a replacement for book module in D5 and also shares some functionality with D6 book module. Book Bridge in contrast is not a replacement to book and works with existing book nodes.