This phrase applies to every human being. When we sense we are judging or starting to judge others then the Bible reminds us to examine ourselves first.
Why is that ? This is best dealt with by Matthew 7:1 to 7:5.
Let us put this to a simple test. Let us say we are face to face with someone. We can see the other's full face but we can not see our own face. In short we are blind to our own selves . We need to look at a mirror first.