The purpose of using an Icebreaker in training / teaching is to allow group participation. It is a good tool to get people interested and feel more relaxed especially when you have a diverse group of students who do not usually work together, or may not know each other at all.
Icebreakers offer a bit of light fun to alleviate any concerns, and help students get to know each other, as well as get students engaged and motivated for the main session.
By getting to know each other and the trainer, students become more engaged in the session and subsequently contribute more effectively, and are able to continue through the course in a more supportive environment.