First off a bit of history that currently adorns my signature on Dragonsfoot:
Frank Mentzer, longtime cohort of Gary Gygax and one of the few active folks from the advent of TSR and the role-playing age on DF. There are people who think of THAC0 as 2nd Edition AD&D creation when in fact according to Frank it predates 1st Edition and may even have been in common parlance around the time of the Lake Geneva Campaign. And again for those that don't know the Lake Geneva Campaign was the grand-daddy of them all in terms of RPGs; it was the one that Gary DM'ed and well, pretty much wrote AD&D as well know it.
Now on to THAC0 itself: THAC0 stands for "To Hit Armor Class (Zero)." In 2nd edition AD&D in melee combat, one rolls a d20 and compares it against their THAC0 score. For example if your THAC0 score is a 18 and you roll a 14 you would hit Armor Class 4. In other words, straight up on the die with no modifiers THAC0 represents the roll you need hit AC 0 on a d20. In a nutshell that's all there is to it. So why is it that people look like this when you bring up the subject of THAC0 in gaming circles?
Seriously simple math is that hard folks? The only argument that I can see possibly being made is for a unified mechanical rule of later editions which THAC0 is not. But, then again 1st and 2nd Edition has lots of wonky bits to it anyways. 3rd edition and later did tiddy up stuff, but abandoned this one when it wasn't broken.Plus I'm not a fan of a single mechanic simply for its own sake.
So the next time so f-tard starts squawking about the difficulty of simple math and unified mechanics being superior just point out the can do math. For the older grognard crowd point out that THAC0 appears in their "Ye Olde Holy Book" aka the 1st edition Dungeon Master's Guide written by Gary. But be prepared to save vs, long winded diatribe regarding about how Gary didn't like it.
Dudes... STFU it's in the freaking book, your book no less.