Loosely-defined, headspace is the "rattle-room" that a cartridge has to move within the chamber once the bolt is closed.
For bottle-neck cartridges: Chambers are factory cut to a specified dimension from bolt face to mid-shoulder (± a few thousandths) depending on the cartridge. If the cartridge case is sized to those exact dimensions, the assembly has "zero" headspace. If the case is sized shorter than the chamber by (say) 0.005", then the excess headspace is that 5 thousandths of an inch.
Rifles are
designed to work best with a few thousandths clearance of headspace. But
many thousandths causes the cases to stretch excessively upon firing, which after repeated reloading may cause stretching beyond the ability of the brass to handle it, and the case separates near the head. -- bad juju.
Headspace is best determined by a gunsmith's use of (3) solid metal headspace gauges machined to exact dimensions.
The "GO" gauge is the shortest and MUST allow the bolt to close. The NO-GO gauge is 6-8 thousandths longer and the bolt is NOT supposed to close on that one. The chamber is therefore between the two dimensions and properly cut to spec.
If the bolt
does close on the NO-GO gauge, then the "FIELD" gauge (several thousanths longer still) is used. If the bolt won't close on that gauge, then the rifle is considered safe to shoot w/ factory ammunition, even though not technically in spec.
If truly excess headspace is discovered, the usual solution is to remove the barrel and machine it to where it will set/screw back into the receiver an additional amount. (Others may know better whether a full turn is req'd for barrels not having a front sight), but usually the gunsmith will then re-cut the (now shorter) chamber to correct headspace specs.