Someone who is inferior in any form is not totally restricted in how they behave in front of a superior. It refers to some freedom that minions take in front of their masters. The phrase talks about the boldness that cats shows even in front of their masters and get them to stroke them.
A cat may look at a king is an English proverb that means even someone of low status has rights. A cat may look at a king implies that all people have certain minimal rights by virtue of being alive. Like many proverbs, the origin is unknown.