Respect for people is a key concept mentioned in much of the Toyota Production System / Lean literature. Variations of it are mentioned in many related disciplines, like Theory of Constraints where I spend a lot of my time. What this phrase tries to describe is that the people who work in the system know a great deal about the system.
Just like "culture," this one is hard to describe by itself. Maybe the actions and behaviors help. (This may be a reason why people think it is "touchy feely.") Showing respect is asking people to participate in the creation of a solution. It's being honest enough to say that I don't know everything. Showing respect can also be challenging people to think differently, or to lead them on a path to learn something new. It's about giving them the space to actually learn. It's about drawing people in.
If we simply tell them what to do - or we ask for their opinion because we are supposed to and then disregard it - this is NOT showing respect.
I came across a video clip recently where someone claims that a bad demeanor or gruff interpersonal style is antithetical to the concept of "respect for people." I think there is a HUGE difference between a personal style and whether that style encourages people to learn and participate. Taiichi Ohno and Eli Goldratt amongst others have been known for their gruff and "difficult" interactions with people. My observations of Goldratt, after getting over the invective, has always been that he pushed people to think. Sure he would get frustrated when it appeared that they were being lazy, but I don't think this shows a lack of respect or a belief that people are stupid.
Come to think about it, what about Steve Jobs. He was classically monomaniacal. Was he showing disrespect for people? Or was he pushing them to their limits? I suppose it depends a bit on whether you were the subject of the diatribe.
Believing in the inherent value and quality of people comes out in how you challenge them and what you expect of them. It has much less to do with your direct personal style.
And p.s. You don't have to be gruff to be an effective leader, either. That's all in the style.