Textile Engineer here,
Basically its called a dobby border.
In some cases there are more than one.
It is above the ‘body’ of a towel.
The main function is to provide structural support, prevent fraying, help maintain the shape of the towel.
It is also a space for branding or decoration.
Various brands distinguish their towels based on their dobby borders (stripes).
Various towels have multiple such stripes just for decoration purpose.
Sometimes when at the very top or bottom they serve as “finish” point for continuous pieces produced on a loom.
The small border at the end of towel is called a hem.
It is usually thin, with the same function of preventing fraying of terry loops and yarns and giving a finished look.