Someone who's self-assured is confident in themselves. It's a lot easier to speak in front of a large group when you're self-assured.
If you're shy and unsure of yourself, you'll never be described as self-assured. The self-assured people in your life are the ones who speak up confidently, stand up for themselves, and are poised and positive. This adjective first appeared in the early 18th century, from self and assured, which shares the Latin root securus, "safe," with the word secure.