Being vulnerable means going with the flow of emotions moving through you instead of attempting to force, coerce, or control the emotions coming to you. Vulnerability in your acting will be the key that unlocks your ability to move audiences with the stories you tell and the characters you portray.
As an actor, your body is your instrument. Keep it unclogged (ie, vulnerable)! Being vulnerable means letting your work and emotions flow easily through you, affect you, and incite you to action. Opening up to this flow allows the audience to perceive your emotions and experiences with clarity.
There are many things (such as fear, anger, resentment, control) that can clog or muddy up your attempts to be vulnerable, and it can take some time and effort; but once you figure out your personal path to the flow of vulnerability in your work, you will have stepped into your power. So keep at it!