When finishing leather edges (to seal and protect them), many abrasives can be used. Along with sandpaper, metal files are another option. With so many varieties available (round, flat, diamond, etc.). They are also available in many grit sizes. For grit sizes, the smaller the size number, the larger/rougher the filing result will be. Likewise, the larger the number the more fine/smooth the filing result will be.
Generally, one would start with a rougher file and work their way down to a finer file as the edge becomes tighter and smoother. Files make it easy to smooth rough leather edges, helping prepare them for further finishing such as burnishing, waxing, or painting.