A squamous cell is a type of epithelial cell that is found in many locations of the body. Although many people think of epithelial cells as "skin" cells, they can actually be found covering many layers of the human body - not just the outside.
Squamous cells are the flat, as opposed to square (cuboidal) or rectangular (columnar), epithelial cells found in many parts of the body. You can find squamous cells in the mouth, on the lips, and on the cervix, as well as in the middle layers of the skin. Squamous cells are pretty utilitarian epithelial cells, used for covering just about everywhere.
Most people only become familiar with the term squamous cell when they are diagnosed with a squamous cell carcinoma - a type of cancer. Squamous cell carcinomas are the most common cancer of the oral cavity and are also commonly found in the cervix and the skin.
Women may also be familiar with the term squamous cell because potentially precancerous abnormal Pap smear results are diagnosed as squamous intraepithelial lesions. In this case, squamous cells found in the cervix have taken on an abnormal morphology, or shape, but they have not necessarily become cancerous. In fact, low grade squamous intraepithelial lesions, or cervical dysplasias, often heal themselves without any intervention.
R. Abu-Eid and G. Landini "Tissue Architecture and Cell Morphology of Squamous Cell Carcinomas Compared to Granular Cell Tumours’ Pseudo-epitheliomatous Hyperplasia and to Normal Oral Mucosae." in Losa GA et al. (ed) (2005) Fractals in Biology and Medicine