Definition:

Vitrification (noun) is the process of melting that clays and glazes go through as they are fired to maturity. In a fully matured clay body, the spaces between refractory particles are completely filled up with glass, fusing the particles together and making the clay body impervious to water.

Vitreous (adjective) is the state of either being or becoming vitrified.

Vitrify (verb) is the activity of becoming vitreous.

Examples:

Vitrification takes place at different temperatures for different clay bodies.

The glaze was becoming too vitreous and might begin to melt off the sides of the pot.

That clay body is still too porous; you need to vitrify it by firing it at a higher temperature.