A smug person is self-satisfied. You can usually recognize someone who is pleased with himself by his smug little smile and self-righteous remarks.
Smug is the opposite of modest and unsure. In cartoons, the smug character often walks around with his chest puffed out and his ego leading the way. “Too much good fortune can make you smug and unaware,” thought Rachel Field, the children’s author. What she means is that successes are appreciated much more when they don't come so often that you begin to feel entitled to them.