This is going to be tough to describe. A 63 finish falls somewhere between a very nice finish (32) and a "good enough for production" finish (125). The finish should be fairly smooth, no chatter.
You might want to invest in a set of surface finish standards, which are simply a set of blocks machined to various surface finishes. These blocks can be used visually as comparators, or used to calibrate surface finish measuring equipment.
Here's one link, there are many more (cheaper) ones out there, I'm sure.