As you get your feet wet with cancer research, you find out that it encompasses all of biology. I'll focus on genetics, because it's what I know something about and the deep relationship between quantitative genetics and statistics gives an obvious point of entrance for someone coming from a quantitative background.
Still, you need cell biology (and physiology, and pathology, and organic chem, but start with cell biology). I keep coming back to Molecular Biology of the Cell (Alberts et al), discovering every few years that the bits I had skimmed over last time turn out to be fundmental. Pay close attention to DNA itself, DNA replication and repair, the cell cycle, apoptosis, cell adhesion, innate immunity, and signal transduction (RAS and PI3K signaling particularly). Everything else is also important, but that gives you something to get started with. For elementary genetics, I liked An Introduction to Genetic Analysis (Griffiths et al) as a grad student coming to biology for the first time; read that whole book or the equivalent.
Introduction to the Cellular and Molecular Biology of Cancer, edited by Knowles and Selby, is a bit closer to the literature than MBoC, but it's very approachable for cancer biology. The chapters are written by experts in the areas, and you get both basic biology as well as clinical topics such as chemotherapy. If you absorb that book, you'll be competent to read well-written general review articles.
If you're focusing on Genetics, my next stop would be Nature Reviews: Genetics and Nature Reviews: Cancer. Their sets of articles on particular topics (look for the "Article Series" links) are quite good. Although there is more opinion in most reviews than a non-scientist might expect, the large reviews in NRG are usually comprehensive, well-illustrated, and authoritative. Pick a few topics to dive into, say susceptibility to sporadic cancers for a look at germline genetics and applications of next-generation sequencing approaches to sequencing tumors for somatic genetics, and start reading. Reviews in Nature and Science are also quite good (and usually have the major benefit of being shorter and more general), though they're much rarer. Reading reviews is harder than textbooks, because some reviews are actually quite focused, and you'll need some context in the field to know how general and objective a review really is. However, if you're serious, it won't be long before you put down textbooks.
For books on bioinformatics itself, I recommend the comprehensive lists posted by Khader and others in response to a request for books on bioionformatics
It's too general and is not a bioinformatics/computational biology question, which is the focus of this site. You'll probably get better recommendations from Amazon reviews.
I disagree that that this question is off-topic, although it is too broad. KSG says he's coming from a CS background. I think helping people who are doing bioinformatics get some pointers to know something about biology-- so they can apply it back to the bioinformatics they're doing-- is a good use of this site. He's not asking for details of a cell line protocol, after all. I'll take a swing at this when I get back from the airport. KSG, you could help by editing your question to clarify why exactly you're interested in cancer and how it relates to an interest in bioinformatics.
Why was this closed?
I really think this question is way too broad. There is no "textbook" to help you understand cancer because we barely understand the disease as it stands. There are so many different aspects of molecular biology associated with cancer that the answers to this question will be completely subjective. For example, there's single nucleotide variations, copy number variations, alternative splicing, gene expression, small RNA (ie. miRNA), lncRNA's, DNA methylation and histone modifications. Without having a defined a specific area of interest this question is useless.
Furthermore, you really need to have a basic foundation in molecular biology / biochemistry / cell biology to really understand the cellular changes that result in tumorigenesis. I'd really focus on reading a few college level bio textbooks (or if you can pick up a few college level courses in night school). I can guarantee you that you won't regret it.