The 'lug width' is the internal width between the lugs of the watch, where the watch strap fits.
Most common lug widths for Nato Straps are 20mm and 22mm. These widths you can find on Rolex, Omega, but also Seiko or Tudor and many more. It is important to measure correctly asonly1mm of difference might result in a strap that is too loose or worse, the strap just doesn't fit.
In thepictureyou can see a graphical representation of the lug width, the lugs and what to measure.