"Publish or perish" is a phrase that means for someone who wants to be a teacher or professor, they need to write lots of papers or books and then get them published so that other people can read them. If they don't do this, they might not get a job or might lose their job. It's like doing your homework, but instead of just showing it to your teacher, you have to show it to the whole world. So, if you want to be really good at teaching, you have to write and share your ideas all the time.