THAC0 (/ˈθækoʊ/, thack-oh) is an abbreviation for To Hit Armor Class Zero (0), and is used as the basis for determining if an attack roll succeeds in AD&D. To calculate if a hit succeeds, the player rolls a 20-sided die, and adds or subtracts any bonuses or penalties. The player then subtracts that number from their character's THAC0 value to find the strongest armor class (AC) the attack hits. In AD&D, armor classes range from 10 at the worst to -10 at the best, meaning a lower THAC0 value will yield better hits.
A player can also subtract the opponent's AC (if known) from their character's THAC0 value to find the roll they will need to hit their opponent.
Example: If the player's character has a THAC0 of 10, and they roll a 12 on the dice (with no bonuses), the best armor class they can hit is -2 (10 - 12 = -2). Put another way, if the same character wishes to hit an enemy with an AC of 4, they need to roll a 6 (10 - 4 = 6). The lower the THAC0, the lower the roll needed to hit any given AC value.
Fighter classes have the best THAC0 progression and spell users have the worst.