At the end of a lesson period, your professor says, "class dismissed." This means that you and the rest of the students are free to go.
Dismiss means to let go. If a judge dismisses a case, it means he's saying it has no merit, and is throwing it out of court. If you are dismissed from your job, it means you've been fired. And if you've been ignoring your friends' warnings that your boyfriend is cheating, you've been dismissing their concerns. "Don't dismiss me!" is something you say when the person you're talking to is not taking you and your comments seriously.