Epithelium lines surfaces and cavities, such as the mouth, throughout the body. Cheek cells consist of a specific type of epithelium: stratified squamous epithelium.
Epithelial tissues are named based on the number of layers of cells included in the tissue and the shape of the cells. The number of layers of cells between the surface/lumen and the basement membrane underlying the epithelium determines whether the tissue is classified as simple (a single layer of cells) or stratified (more than one layer of cells). Psuedostratified epithelium appears to the eye to be stratified, but all of the cells are attached to the basement membrane so the cells are actually all in one layer. Cheek cells are arranged in more than one layer and, therefore, the tissue is considered to be stratified.
Epithelial tissue is also named based on the shape of the cells in the tissue. If the tissue is stratified, the shape of the most superficial (top) layer is used to approximate overall cell shape. The different shapes include squamous cells (thin, flat cells), cuboidal cells (cube-shaped cells), columnar cells (rectangle-shaped), and transitional (stretchy, balloon-shaped cells). Because cheek cells are thin and flat, they are classified as squamous cells. When you put this together with the number of layers, you have stratified squamous epithelium.