A critical hit (crit) occurs when your unmodified attack roll results in a number in your weapon's critical threat range and is confirmed with a confirmation roll. Crits deal extra damage according to the critical hit multiplier of your weapon.
If you hit your target while getting a (non-modified) d20 roll within your weapon's threat range, this results in a critical threat (even if your modified attack roll wouldn't beat the opponent's AC).
A critical threat means you have a chance to score a critical hit. To do so, a confirmation roll is made, with the same to-hit bonus being applied (plus extra confirmation bonuses such as Seeker, Kensei enhancements, Fighter Critical Accuracy, etc.); in this roll, 1's do not automatically fail to hit. This roll must beat the target's AC in order to confirm the critical hit.
If that roll also results in a hit against the target's AC, the critical hit is confirmed, and the base damage is rolled once for every critical hit multiplier. If the confirmation roll is a miss, then the attack is not a critical hit and is rolled as a normal attack (IE, auto-success on natural 20 or test vs. AC for non-20).
For instance a +2 longsword doing [1d8] + 2 damage on a normal hit will do 2[1d8] + 4 damage on a critical hit since it has a 2x critical hit multiplier. On another hand, a +3 greataxe doing [1d12] + 3 damage on a normal hit will do 3[1d12] + 9 damage on a critical hit, because it has a 3x critical hit multiplier. Your strength bonus, enhancement bonuses, and seeker bonuses are also counted as part of the base damage, and thus multiplied by the critical hit multiplier.
Additional damage is generally not rolled multiple times (such as elemental, alignment, bane, or sneak attack damage), except when specified in the weapon's effect description. (For instance burst weapons do additional elemental or alignment damage on a critical hit.) Seeker enchantment improves the roll to confirm the critical hit and also adds to the base damage before the multiplier.