It is a recent movement in ELT, started by a group of teachers who are against 'resource heavy' teaching, arguing that if learners are not interested they will not learn and therefore all material should be generated by the learners and the lessons directed by them, rather than the teacher.
Learners come to class discussing something that is in the news. The teacher encourages and facilitates discussion and provides answers to questions about grammar and vocabulary as they arise.
In the classroom
In a Dogme lesson, the classroom as such does not exist, as there are no resources, course books or lesson structures apart from those that learners bring. The teacher involves the learners in deciding on their priorities each lesson, and takes the role of facilitator of their objectives.