It means, basically, to stand by what you believe. Your character is who you are, as an individual person, and that is based on your fundamental beliefs of right and wrong (morals and ethics) and your basic world view (how you see things). If you truly believe those basic things, then you should still believe them even if someone disagrees (is in opposition).
However, there has to be some openness to changing views if the argument is valid. Your world views might not be correct (no human being is always correct about everything). It is just that most of us have world views that are based on a lot of evidence and thought, so changing them would require some pretty darn good arguments.