Many voice teachers to sing, "on the breath", "forward", "spinning" and so on. At the crux of the issue that all of these subjective ideas are trying to address is the Valsalva maneuver. The discovery of the Valsalva maneuver's negative effects on singing was by my teacher Dr. Tom LoMonaco. This subject is a big part of his book as well.
The Valsalva maneuver is a medical term. There are two kinds of Valsalva maneuvers. The first is commonly referred to as the bucco-nasal Valsalva. A good example of this is when your ears feel plugged and so you hold your nose closed with your hand and your mouth closed while trying to blow air out. The other Valsalva - the culprit in constricted singing - is the laryngeal Valsalva. This maneuver happens when we lift something heavy, cough, laugh, sneeze, when women give birth, or - excuse the crudeness - when we go to the bathroom. It is the closing of the glottis while forcing air out against it. While this may be good to help us lift a heavy rock, it does not work in singing. In fact, it greatly inhibits the free vibrating ability of the vocal folds.
So, as singers we must find a way to completely circumvent this maneuver. That is done through the proper coordination of the breathing muscles. This refers back to the the ideas used by many teachers to sing "on the breath" or "spinning" the sound. Also, the attempts for the teacher to stop the student from "pushing" or singing "in the throat" or "too far back". These are all attempts to address the Valsalva maneuver. But they do not directly address it and therefore the results are usually poor. Many teachers today bypass fully engaged, big singing because it tends to cause a student to "constrict" or go into the Valsalva maneuver. Since we can understand what causes the Valsalva and how to disengage it, there is absolutely no reason why a singer cannot sing completely engaged, big and free. That is historically what all the great singers did. They all had very little constriction in the sound while keeping the voice fully engaged and free. Therefore, I will be also blogging about the proper engagement of the breathing muscles and the proper development and use of the vocal registers. This is another crucial part of great singing.