"...What's "headspace"?..." It's a rifle manufacturing tolerance that allows any maker's ammo to be used in any rifle/firearm of like chambering. Each type of cartridge, rimmed(.303 British), rimless(.30-06), belted(.300 Win Mag), straight walled pistol/rifle(.45 ACP/.30 Carbine), headspaces on a different part of the cartridge.
A rimmed cartridge headspaces on the rim, a rimless on a spot in the chamber usually where the shoulder area, a belted magnum on the belt, a straight walled pistol/rifle on the case mouth.
Headspace is checked, not measured with precision made guages that mimic part of the cartridge. A .303 headspace guage(there's actually a set of 3.) looks like the bottom inch or so of a cartridge. The 3 are a Go(minimum), No-Go(low end max) and Field(absolute max). They run $26 or $30 US each, depending on the maker. Clymer or Forster.
To use 'em, you either remove the extractor or slip the guage under it and gently close the bolt. The bolt should close completely on a Go, but not on a No-Go. However, if it does close on the No-Go, try the Field. If the bolt completely closes on a Field, the headspace is excessive and the rifle is unsafe to shoot with any ammo. The Go guage is normally used only when fitting a barrel. So you can just use a No-Go and/or a Field.
Spent cartridges with bits of tape stuck on tell you nothing.
If the headspace is excessive, the cartridge can rupture, sending hot gases and sometimes bits of cartridge, back into the receiver and your face(always wear shooting glasses. The hide of your face will grow back or a skin graft, usually taken from one's butt, can be done. Your eyes will not.). The bolt lugs can shear off, sending the bolt into your head. That'd be a worst case thing though. You'll have indications of excessive headspace long before that'd happen. Flattened primers, difficult extractions, case head cracks, et al.
Not enough headspace won't allow the bolt to close when a cartridge is loaded.
Here's a good article with pictures that explains it better. The Surplusrifle site is your friend.
http://www.surplusrifle.com/shooting/headspace/index.asp
After all that, most milsurps, unless they've been abused, don't have headspace issues. It's not a bad idea to check it anyway. Gets expensive if you're buying different calibre firearms. Most cartridges require a different guage. It doesn't matter what rifle you're checking though. .30-06 is .30-06.
Lee-Enfields can have headspace issues. The bolt head(they come in 4 different sizes. Changing and checking with a guage is how headspace is adjusted with Enfields) comes off easily or was put on without using the guages. You never know what has been done to any milsurp, but especially Enfields. Matching serial numbers(bolt and receiver) does not guarantee good headspace either.
No. 4 Rifles are easier to adjust than a No. 1. No. 4 bolt heads are numbered 0 to 3. You just try the next number up with a guage. No. 1 bolt heads are not numbered and you need a handful to try with the guages. Gets pricey. $19 each from Marstar for No. 4 bolt heads. Mind you, #3 bolt heads aren't easy to find. No. 1 bolt heads are not easy to find, period. Marstar wants $20 each and you have to tell them what length you want. Sometimes you can try replacing the bolt body. They can have different lengths. That isn't cheap either though.