Most everyone has done a good job of explaining what the measurement is refering to on barrel links.
Here's some other things to keep in mind when dealing with barrel links.
Don't take for granted that a number 3 link or any number link for that matter will corespond with the correct amout of thousands that it desinates.
I highly advise you measure all links before using them.
Going to a longer link in most cases will give a little more lockup to a barrel.
However just going to a longer link may not be the answer because when you change barrel links you change the timing of the gun.
The longer link may make the lower lug of the barrel strike the VIS to soon as the barrel is trying to unlock from the slide, doing so will damage the barrel and slide.
Going to a shorter link may cause link failure because the barrel may be stopping it's rearward movement on the link only.
There's much more to 1911 barrel links and barrel fitting then most people understand.
My advise is if you are not well versed in the timing of a 1911 pistol leave the barrel link alone.
Best Regards
Bob Hunter