As ceramic bodies vitrify in the kiln they become more dense with temperature (shrinking in the process). A wide range of particle types typically exist and they react to heat differently. Some melt and flow. Some alter their shape as they transform mineralogically. Some react with others. Some partially dissolve. Some remain inert. When the matrix reaches the point at which the lowest "clay body porosity" is achieved they have reached maximum density. Firing beyond this point entails issues that need to be understood. Certain bodies can tolerate it, others will begin to expand, blister, bloat and melt. Or just become more brittle.
Density is also a consideration in refractories. Since particles do not melt the fired strength derives only from the density imparted by particle size distribution and particle bonding imparted by the sintering process. Much effort goes into selecting (and calculating) material particle size distributions that will pack together well. Not only that but more points of contact that can be produced the higher the strength with be.
The term vitrified refers to the fired state of a piece of porcelain or stoneware. Vitrified ware has been fired high enough to make it very strong, hard and dense.