A texel is the smallest unit of measurement for space on a texture map. It is similar to pixels which are the smallest unit of measurement on a physical monitor screen.
Texel: commonly a unit of measurement in your 3D scene i.e. centimeters
Texel density describes the relationship between different textures on different meshes in your 3D scene. Texel density is a formulaic relationship that describes the number of texels (units) that a texture map is divided into. Formulaic, it looks like this:
$$ 1024px/100cm = 10.24px/cm $$
$$ TextureMapSize/Texels = TexelDensity $$
$$ 4096px/100cm = 40.48px/cm $$
$$ 2048px/100cm = 20.48px/cm $$
$$ 1024px/100cm = 10.24px/cm $$
$$ 512px/100cm = 5.12px/cm $$
$$ 256px/100cm = 2.56px/cm $$
$$ 128px/100cm = 1.28px/cm $$
Texel density is used by art directors and technical artists to control the level of detail in textures that appear on-screen between meshes, reducing mismatch between those textures to create a more consistent look for the audience. An example is demonstrated below using grid textures: