"Engagement" remains a popular business term, although it's not so new. By the way, aren't business people faddish? When you come across a new term in a meeting or an article, you can count on hearing it repeatedly until it runs its course.
I remember first hearing, "engaging the workforce" a few years ago. Workforce engagement happens when employees are more involved than just showing up. They get it or are into it. They're involved in their jobs and what your company is trying to accomplish. They support the direction their team or company is taking. Now I hear "engagement" applied to various business relationships -- customers, partners, suppliers. I recently heard a college administrator discuss "alumni engagement".
Customer-facing workers being engaged would seem to be the first step of customer engagement. As a customer I think you can always tell when someone seems less than engaged serving you. If it's too much for them to be excited about their jobs, front line people should at least care about what customers are experiencing.
Showing customers you care goes a long way, especially in problem situations. Doctors had to learn bedside manners. Now in the economic downturn, even attorneys are being forced to learn and practice customer service. In this article, one lawyer had been directed for the first time ever to follow up on past clients, and was stunned to learn they not only appreciated it, but sometimes had further business to render. The lawyer concluded, "Everyday I need to be thinking about these existing clients."
That's actually a good mantra for any customer-facing professional.