The significance of cross-site scripting (XSS) in web security lies in its potential to allow attackers to inject malicious scripts into web applications. This vulnerability can lead to unauthorized access to user data, session hijacking, or the spread of malware. XSS exploits occur when a web application does not properly escape or validate user input, allowing attackers to execute scripts in the context of other users' browsers. Mitigating XSS risks is crucial for safeguarding sensitive information and maintaining user trust.