This was the required text in a course I just took in discrete mathematics, and it is very lacking. The descriptions are not detailed enough for first-time learners of the material. Biggs tries to cover very many topics, and as such, doesn't cover any given topic thoroughly. The book feels like random snapshots of various components of discrete mathematics, but not all of the snapshots are representative of the topics to which they belong.
For one group of chapters, Biggs discusses things which are only really relevant or applicable in computer science (or, at the very least, given a computer). This is to be expected - discrete mathematics and computer science go hand in hand. Unfortunately, though, it does not appear that he is a practicing computer scientist - he omits the names behind some of the famous algorithms, i.e. Dijkstra's shortest path algorithm and Prim's minimum spanning tree algorithm. He ditches the minimum spanning tree problem and proceeds to DFS without discussing Kruskal's algorithm. He also performs heap sort with a min order heap, sorting elements in ascending order, which, as most computer science students should be able to recognize, requirs linear-order extra space in order to copy the final array (as opposed to using a max-order heap, which requires only constant space). He uses a seemingly FORTRAN-based pseudocode, but omits symbols, adds more English words (as if FORTRAN didn't have enough), and uses no comments.
All in all, avoid this book if possible. For introductory-level discrete mathematics, I would recommend Discrete Mathematics and Its Applications, which still sits on my shelf and serves as a great quick reference. For introductory-level data structures and algorithms, I would *highly* recommend Data Structures and Algorithm Analysis in C++ (3rd Edition), which has extensive diagrams, examples, analyses, proofs, and even some fully coded implementations to help jump-start readers as they get more comfortable with ADT use (also available for C and Java). However, no book is ever a substitute for going to school :-P.
I hope the Biggs book is never mandatory for any of your classes.