Reaction

Reaction, or NPC Reaction, refers to how an NPC reacts to interaction with a player-controlled character. This reaction is controlled by three factors: The resulting Reaction score, from -7 to +21, determines such things as vendors' prices, whether a normally friendly NPC will turn hostile and attack you, or whether an NPC will give you a side quest and sometimes whether he/she will give extra rewards for completing the quest.
 * 1) Luck. The computer generates a random number between 8 and 12 (a terribly un-d20 range; 1d5+7? ewww!). Adjustments are then applied to this number:
 * 2) Reputation. A reputation adjustment value ranging from -7 (reputation 1) to +4 (reputation 20).
 * 3) Charisma. A charisma adjustment value, normally ranging from -8 (charisma 3) to +5 (charisma 18).

Note: Vendors' prices are affected by the Reaction score of the party leader (the top character on the right-hand side of the game screen), not the character who initiates dialog or the character currently selected.

Or Not
Luck may not be a factor. On your character's Record, at the bottom of the Abilitiy Bonuses section, there is a Reaction score that corresponds to a fixed value of 10 with the adjustments applied. This appears to be a fixed score, not the average ±2 that the manual describes.

According to a widely-quoted source,  NPC reaction was not implemented as the manual states, but rather a constant value of 10 is used as the base value, and the reputation adjustment actually ranges from -20 to +4.

There are also many situations in the game that are affected solely by Reputation or Charisma alone, rather than by Reaction. These are listed in the Reputation and Charisma articles.