Gotham is overtaken with nasal production; it's heard on Broadway, onstage at the Opera, and in a certain musical at the cinema around the corner. Old School voice teachers ridiculed it, considering it one of two chief defects, the other being guttural timbre. Of course, they are often heard together; like the characters in Samuel Beckett's Waiting for Godot, they argue and fight with each other, the nasal voice thinking he's better than his lowly, throatier partner. However, each constrict the path towards clear tone.
Tenors are often the worst offenders. Sure. The voice may penetrate, but it's never beautiful, and incapable of soft-toned mezza voce singing. Whining away, all bang and no buck, its purveyor is often stuck with comprimario roles and lesser fees. Baritones and basses do it too; snarling away at full volume, they sound particularly hollow when nuance is needed since nasality typically functions in an all or nothing fashion. High notes? Forget it. They are muffled and the voice effectively muzzled.
What brings this kind of production about? Mechanically speaking: the soft palate is lowered, while the 'singing position' is compromised. The 'singing position' itself entails a rounding of the vocal tube, which the audition of a clear, deep and resonant vowel achieves without a lot of hoo-ha. The clear vowel has to be present in the mind's ear, and the teacher who can demonstrate it gives the student a great deal of information. Exaggeration can work wonders, especially if the student is encouraged to play with tone and feel the result. Making the voice really, really nasal and then clear? This often elicits useful realizations.
Oh...it goes up back there!
It opens up!
The clear vowel has lots of /i/ like buzz, which can be confused with nasality. As such, the nasal singer has the wrong idea of voice placement. The different is between singing in the nose and singing through the face; between the voice feeling nasal and sounding nasal. You are on the right tack when the voice feels buzzy, yet sounds very, very clear.
Where does one hear a clear vowel? At the upper lip, the so-called Center of Singing, where bone (buzz) and air (clear) conduction meet.
Illustration from Lilli Lehmann's "How to Sing."