One of the biggest concepts in (successful) vocal pedagogy is that the students needs to physically experience in an overt, non-subtle way what it is you are trying to help them do.
To explain - learning how to sing is a process with many, many small steps. Each step is (usually) an actual physical achievement, even though they may not be perceived as such. For instance, if you asked someone to sing something sadly, or brightly - even though those are abstract concepts, you have to make physical adjustments with muscles and such to do so.
So - when you are trying to help a student learn the next step, they need to clearly feel and understand what it is you are teaching them to do. You can guide them blindly with exercises (as many teachers do), but that's not really helpful because they won't know how to recreate it on their own.
Sometimes this is very hard to do. We don't have direct control over the muscles that we use to phonate; we can only make adjustments with our tongue, jaw, etc. So, it's beautiful when nature provides a very, very clear way to demonstrate what it is you are wanting to do. One of the lovely examples with this is demonstrating to male singers the difference between their chest voice (the lower, heavier part of their voice) and head voice (the higher, lighter part of their voice).
I'll spare you the physics/acoustics lesson, but suffice it to say, by the nature of how you create the sounds, certain vowels encourage singing in the head voice, and other vowels encourage singing in chest voice. For men, singing a "heady" vowel in the top of their range, then singing a "chesty" vowel in the bottom of their range provides such a crystal clear example of the difference between the two parts of their voice (called "registers").
I love the look on a new singer's face when you have them do this. Singing is sometimes so abstract and confusing, but then you have these moments of clarity and, well, out of nowhere, the light begins to shine.