Technically it's not that it had to be manufactured before the date (which is May 19, 1986). It's that it had to be in the NFA registry before that date. Someone, somewhere, had to get an NFA tax stamp legally on the weapon in question before that date, but afterwards the gun can be bought and sold (you do have to update the info in the NFA registry as to who owns it currently). If the weapon was mfg'd before the date but not registered in the NFA registry, you can't ever buy it as a normal civilian.
As noted in another post, for full autos not already in the NFA registry, you have to be a Class III dealer (getting this license generally requires proving you have LE/mil sales contracts, and keeping up that proof), a manufacturer (who obviously can test their own guns), or obviously be issued one by a government entity for duty use.
The net effect for us "regular" civilians is that there is a finite, limited pool of full autos that were on the NFA books prior to 1986, and those are the only ones we can buy/sell/trade between each other. Over time the pool dwindles as guns fall apart, get destroyed, or get "lost" (someone dies and forgets to mention their NFA collection buried in some box in some basement...).
This tight supply problem makes these guns very expensive. A registered Colt M4 that should by all rights be worth about $1,000 ends up selling for ~$12K+, etc. You can see some prices at
the NFA section on subguns.com. Note when you see cheap prices there, usually you'll click into the item and see it's a dealer sample only (requires Class III license, not for normal folk).