A good general background on application security issues, unsurprisingly, is contained in The Art of Software Security Testing, co-authored by Veracode cofounder Chris Wysopal. The book goes beyond the basic description of classes of application security vulnerabilities into specific recommendations for testing strategies and ways to improve the software development lifecycle to avoid introducing vulnerabilities.
There have been a few pivotal written works about how certain classes of software vulnerability work. The canonical one is the Cult of the Dead Cow’s “The Tao of Windows Buffer Overflow,” written by veteran hacker Dildog. Written in a clear and easy to read (if profane) style, this work should scare the living bejeezus out of you.
There are some more business friendly summaries of other vulnerability classes available. One source for this information is Veracode’s own web site, which features clear explanations of SQL injection and cross-site scripting (XSS).