The selvage (US English) or selvedge (British English) is the term for the self-finished edges of fabric.
The selvages keep the fabric from unravelling or fraying.
The selvages are a result of how the fabric is created.
In woven fabric, selvages are the edges that run parallel to the warp (the longitudinal threads that run the entire length of the fabric), and are created by the weft thread looping back at the end of each row.
The terms selvage and selvedge are a corruption of "self-edge", and have been in use since the 16th century.