A vector logo is drawn as shapes and curves rather than a fixed grid of pixels, so it can be scaled to any embroidery size without softening or breaking up. That matters because the same mark might be stitched small on a chest and larger elsewhere, and we want both built from the same clean source.
The usual vector formats are AI, EPS, SVG and vector PDF. If your logo was professionally designed, a vector version may be held by your designer, signage supplier, printer or whoever manages your brand assets.
One thing worth knowing: a vector file is source artwork, not an embroidery file. It cannot be sent straight to an embroidery machine. It is the ideal starting point from which the stitch file is built.