Illustrator, Inkscape and online converters all offer an automatic trace. It follows the pixels, so the result carries hundreds of points, uneven edges and a spread of almost-identical colours.
On screen that can pass. At the printer the colours won't separate, on a vinyl plotter the blade judders along every bump, and enlarged for a sign the edges look lumpy. Redrawing by hand gives deliberate curves with as few points as possible, closed shapes and one object per colour.
Need a stitch file for an embroidery machine rather than print artwork? That is digitising: see logo digitising for embroidery.
The quality of your image matters less than you'd think. We redraw the artwork instead of tracing pixels, so a small, blurry or faded file is usually fine: send what you've got.