"What is thickness" is not an unreasonable question. But "thickness" isn't the standard means of describing conductors. Cross sectional area is (in terms of mm2, kcmil, AWG, etc). Obviously in theory circular conductors have a simple relationship between diameter and area. But copper is ductile and changes shape pretty easily, so any measurements you do with a caliper/micrometer is not going to prove much.
That's not to say that the actual "thickness" of the wire is irrelevant. It matters a lot when it comes to terminating the wire, especially with larger conductors. Recently I found that changing from a "normal" 8awg stranded wire to a fancy 8awg wire with a very high strand count made it impossible to crimp my 8awg terminals. The new wire was certainly 8awg in electrical terms, but not in mechanical terms.