THAC0 (pronounced like the sound of a sword hitting an orc in the head) stood for To Hit Armor Class Zero. Prior to 3rd edition, Armor Class started at 10 and went down as better defenses were applied, with an "upper" limit around -10. Hitting a target required rolling a twenty-sided die, adding modifiers, and then comparing the result to a number on a table that cross-referenced the target's armor class (AC) and the attacker's class and level. This took up as many as three pages depending on what version of D&D you played. This was a pain in the ass, but it was soon figured that since the tables' progressions were all linear, you just needed the number to hit zero and work the rest out using basic algebra.
And that final point seems to bug some old-schoolers. THAC0 worked either one of two ways. The first was you subtracted what you rolled from your THAC0 and that gave you the AC you hit.
THAC0 - d20 = AC
The other way was to subtract the target's AC from THAC0 to get the number you needed to roll.
THAC0 - AC = d20
If you took Algebra I, you will notice that both equations are the same. But I never understood why using either of these methods were difficult. Granted I'm an engineer and have taken a metric ton of math, but I learned this in the sixth grade. The other thing that gets people is the concept of subtracting negative numbers. Whenever you add a negative number, it is the same as if you subtracted it's positive counterpart.
10 + (-3) = 10 - 3
Likewise, subtracting a negative number is the same as adding its positive.
5 - (-4) = 5 + 4
I have seen so many people my age that are flabbergasted at this concept. Like I said, I took Algebra I in the sixth grade. I assumed that this was taught to all students by the time they graduated high school. Why is this such a hard concept to figure out?
This is not to say that I don't appreciate the switch to ascending AC in 3rd edition. It is a bit more... simpler method. But it does disturb me that the trend in role-playing games has been to not challenge people to do better. It starts with dumbing down the math, then it's new abilities every level, and now the train of thought is to never let the PCs fail at anything no matter the circumstances. If I stand for anything in gaming, is that it should be a means to expand your mind as well as entertain you. Take away the thinking, and you might as well be watching a mindless action movie.
The popcorn's cheaper at the gaming table.