It is the confidence in your work, and ability, to perform a given task, to a sufficient degree of competence.
Professionalism is not holding a qualification, or wearing a suit, it is a behaviour and responses to a given set of situations. It can even mean just being a human, and offering some common sense, and emotional intelligence.
Is it unprofessional to cancel a meeting when you are unable to attend? No. But it would be considered unprofessional if you cancelled without some sort of advance notice, or message. Even if someone didn’t like the fact that you had to cancel.
The fact that none of us are perfect means that it’s ok to have moments when your caught off-guard because of life’s random surprises. As imperfect beings we are bound to fail sometimes, and that’s ok if we are learning from those mistakes.