Ed. Leadership article from 2008). The term was coined by J. Kleinfeld in 1975. It refers to a teaching personality that makes an emotional connection with students, but also expects high academic and behavioral results from students. This teaching technique has been praised as being particularly effective for poor and minority students; students who have historically achieved at much lower rates than their middle-class, white peers. (see Becoming Warm Demanders, Caring Teachers, and Warm Demander Pedagogy)
Some teachers would argue that their job is only to teach and not to develop caring relationships with their students. But I would counter-argue that only a part of a teacher's job is to teach. The more important part is to ensure that students are learning. This, indeed, is the hard part of teaching. There is no single teaching strategy that is effective for all students when it comes to ensuring that learning is taking place. Instead, we have to look to our colleagues and look to research and look to best practices to find these most effective teaching strategies.
We know that students respond better to those teachers that show a genuine interest in them. Students want to make their teachers proud of them--especially the teachers that really care. Teachers that that understand their content and do not understand the need to connect with their students, often see lower academic results from their students. And teachers that are very caring and friendly with their students but demand only low-level skills (similarly) see low academic results.
It takes both: Warm and Demanding.