In computer security, the term White Hat is used to describe a security expert who specializes in penetration testing and system hardening. This is opposed to a Black Hat that would have more nefarious intentions for his/hew knowledge when put to practice.
The term White Hat is associated with Ethical Hacking. A White Hat researcher may test the security of an organization using a barrage of different attack methods. An obvious start is scanning networks and systems for known vulnerabilities and weaknesses, or testing their resistance of denial of service (DoS) attacks.
Another target are the people with access to an organization's resources, such as employees. By employing social engineering tactics by phone or e-mail, White Hats may be able to get sensitive information such as login credentials. Even dumpster diving - digging through the trash to find documents with sensitive information that might help penetrate an organization's systems - is not out of the question.
Basically put, the White Hats in the digital world, are the good guys.