A logo is cut using what is called a vector file format, such as file types svg, eps and ai. The data in files of these types can be thought of as curves and lines defining the outline of the components in the design. If you have a file of this format available, that avoids the need for conversion.

More common files such as jpg, png and bmp, are rasterised file formats, comprised of individual pixels. If you only have a file of this type, then the higher the resolution, the better. A good quality, high resolution file can be converted into the necessary vector file format.