Copper dimension around the PCB component's hole (pad?)
The exposed copper around a through hole is called the annular ring. The annular ring should be appropriately large to accommodate solder-to-pin wetting.

Your PCB fabricator should specify a minimum annular ring size, so be sure to check that. For example, OSH Park specifies 0.127mm (5 mil). Otherwise, when you design your PCB, you can generally add 0.25 to 0.30 mm (10 to 12 mil) to the hole diameter. (There are IPC standards such as IPC-7251 which you can follow if you need/want to.)

Conditions where you may want to increase the annular ring size:


Component needs physical strength, such as a connector or bulky heatsink
Component requires a large amount of current
Component will be soldered by hand or some other less-precise operation


Annular ring size decrease or modification would be due to:


Pitch or proximity of other pins on the component. Often oval pads are used when extra surface area is needed, but other pins are too close to allow a circular shape.
Other considerations such as solder bridges (depending on process)


For more information, see: How to determine annular ring width for thru-hole pads?