Definition
To protest about something which appears to be unjust.
How People Actually Use It
Someone who strongly disagrees with another person's fair opinion/criticism. It came from is a baseball term, "foul ball".
"John Doe: Justin Bieber acts like a arrogant fool all the time. He sucks. Jane Doe: No, he isn't. He is a talented singer. John Doe: Did you just cry foul?"
Source: Urban Dictionary