In this quote, Walt Whitman is discussing one of his favorite themes, and that is the concept of celebrating who he is as a human being, even if it is flawed, contradictory, or imperfect. Whitman was an individualist, a man who emphasized loving oneself and seeing oneself as the source of great strength and guidance. Whitman, along with Ralph Waldo Emerson and Henry David Thoreau, felt that the person who could judge best and understand best was our own selves. They believed in taking pride in one's opinions and beliefs and decisions, even if they were to change those opinions or beliefs the next day.
Walt Whitman admits openly that he is contradictory, meaning, he says one thing one day and the total opposite thing the next day. He isn't consistent in his opinions, and that is okay. Being contradictory is a part of human nature, and we shouldn't be embarrassed by it, but embrace it, because it is who we are. He goes on to say that within his own person there are "multitudes" of different angles and personalities. We all can relate to that feeling--at home we might be open and talkative, while at school maybe we're reserved. Or, maybe with our friends we are super fun and crazy, but with our teachers we are respectful and quiet. So, each of us contains different parts of our personality that come out at different times, and Whitman emphasizes being okay with that, embracing that part of ourselves, and loving ourselves for who we are.
I hope that those thoughts helped; good luck!