The 'lug width' is the internal width between the lugs of the watch, where the watch
strap fits. Most common lug widths are 20mm and 22mm. It is important to measure correctly as only 1mm of difference might result in a strap that is too loose or worse, the strap just doesn't fit.
In the picture you can see a graphical representation of the lug width, the lugs and what to measure.
If you have any doubts, just let us know!