If you're self-possessed, you always seem to be calm and confident. It's easier to be successful as a substitute teacher if you're self-possessed than if you're nervous and uncertain.
Someone who's particularly poised can be described as self-possessed. It's a hard quality to fake, but a worthwhile one to aspire to; other people tend to take you more seriously if you're self-possessed. The adjective self-possessed and noun self-possession first appeared in English around 1740, with the sense of "(in) command of one's emotions."