The importance of the guage number (size) is that it expresses the amount of current that the cable can safely carry without overheating or excessive voltage loss.
Normally a lower gauge/higher capacity cable will also be phyiscally larger (greater circumference), but this is not always the case.
What is really being measured is the amount of copper (or other conductors) encased within the extension cord. It is possible to have a lower gauge (larger) cable that is not actually larger than the next smaller size because the outside (jacket) is thinner.
In most environments, a 14 gauge extension cord is safe up to a 1500 watts of total load, while a 12 gauge cable can handle 1800 watts.