A character's Base Attack Bonus is pretty self-explanatory: It's the total Attack Bonus they've received from leveling up in various classes. Other factors will go on to modify this role in combat, including weapon choice, feats, bonuses from magical weapons and items, the use of various abilities, ability score modifiers and circumstance bonuses (flanking, invisibility, etc.) and spell buffs.
While a lot of things go into your Attack Bonus to arrive at the final score, the Base Attack Bonus is a relatively simple matter of tallying up the bonuses gained from your class levels. As with Saving Throws there are only a few different rates of progression: High Base Attack Bonus (warriors), Medium Base Attack Bonus (clerics, rogues) and Low Base Attack Bonus (arcane spellcasters).
Base Attack Bonus by Level
|Level||High Growth Rate||Medium Growth Rate||Low Growth Rate|
|Growth Rate||Rough Class Multiplier|
|High||Class Level x1.0|
|Medium||Class Level x0.75|
|Low||Class Level x0.5|
Not only does your Base Attack Bonus play a significant role in determining your Attack Rolls (and hence your prowess in combat), but every six points of Base Attack Bonus will allow the character to perform a second attack when attacking as a Full-Round Action. This second attack is made at an Attack Bonus five points lower than the first attack, and should a character gain a high enough Base Attack Bonus for a third attack, it's made five points lower than the second attack, and ten points lower than the first. For example, a 6th-Level Fighter has a Base Attack Bonus of +6/+1; their primary attack has a +6 Base Attack, while their second attack receives a +1 Base Attack Bonus. A character's Base Attack Bonus, then, is one of the primary factors that determines how well that character will perform in combat, with primary combatants (typically warriors) gaining a higher Base Attack Bonus, more attacks per round overall, and they'll also gain these extra attacks quicker.