I can't remember when I first heard that instruction for students, but I keep thinking about it this year because I'm teaching the freshman voice class.  Students who come to college to study voice often have very limited ideas of what the human voice can do, and particularly what their own voices can do.  Unless they grew up hearing good singing in many styles, they may have a vocal self image that excludes many useful vocal techniques.  

What does it mean to say it like a singer?  To voice teachers that instruction generally means a resonant speaking voice with excellent diction.  To young singers it might mean something else entirely. 

Another thing that new students struggle with is the idea that what they hear when they sing is usually not what the audience is hearing.  They quickly catch on when they remember the first time they heard their recorded speaking voice.   Their voice teacher stands in for their audience and helps them fine tune what they are doing while it's happening so that they can learn how the best technique feels when they are doing it.  Singers have to learn to sing by how it feels to them -- which may be entirely different from the teacher's sensations in a similar situation.   

Eventually students and voice teachers are speaking the same language, but sometimes it takes a few lessons to get on the right page.