In a new class students may well not know each other yet (and nor will you know them). They may well be shy about speaking also. An ice breaker is designed to overcome this. Good ones will relax the class and create a friendly atmosphere. They will also allow you to get a good idea of the level of the class and see how different students work together (or not, as the case may be).
An ideal ice breaker will, therefore, be fun, simple and productive.
See also, Warmers or Lesson Starters. These are activities to start of a lesson and get the class in the mood for what is to follow. We use the term "ice breaker" only when we talk about students who don't know each other yet; once they get to know each other we'd use warmers to start a lesson.