A thin Font is a single-line font. A person can put a pen, crayon, or a number of tools right into the "claw" of a cutting machine rather than a blade and use the machine to "draw" instead of "cut". When you do that with a regular font (.ttf or .otf) the machine traces the outline of the font so rather than having a single line, you get a double line.
When you use a font (.ttf or .otf file) on your computer, it will typically look something like this example (unless it is an outlined version of a font):
When you use a font (.ttf or .otf file) in the software of your cutting machine, it will trace the outside perimeter of each letter and typically look something like this example):
Thin fonts are created so that a cut machine does not trace the font but makes them with single strokes much like you would if you were writing.