Threat roll

When you take a swing at your opponent, if your NATURAL (un-modified) to-Hit roll is within the threat range AND your modified roll is a hit (WITHOUT invoking the '20 always hits' rule), then you have scored a critical threat. A re-roll is then made with the SAME to-hit modifiers, and if the re-roll is also a hit, then your swing was a critical hit

Some Examples:

A) A Fighter level 5 (BAB +5, +5 to-Hit) with 18 STR (+4 to-Hit), Weapon Focus (+1 to-Hit), and a +1 Longsword (+1 to-Hit, Critical Threat range 19-20, multiplier x2) is fighting an opponent who is NOT crit-immune... say a Goblin, AC:16.

The Fighter has a total to-Hit bonus of +11 (+5 BAB, +4 STR, +1 Wpn Focus, +1 sword). If he rolls (on d20) 1-4 he misses the Goblin's AC:16. If he rolls 5-18 he hits, for normal damage. If he rolls 19 or 20 (within the Critical Threat range of his Longsword), then he hits, and a re-roll is made with the same to-Hit modifiers (+11 vs AC:16)... if the re-roll is 1-4, it's just a normal hit, but if the re-roll is 5-20 (the span he needed to-hit in the first place) then it's a Critical Hit for double damage.

B) A Rogue level 10 (BAB +7), with 14 STR (+2 to-Hit), Weapon Focus (+1 to-Hit) and a Keen (doubles Critical Threat range) +1 Rapier (+1 to-Hit, Critical Threat range 15-20 because of Keen, Critical Multiplier x2) is fighting a Boss NPC (not Crit-immune, of course) AC:28.

The Rogue has a total to-Hit bonus of +11 (BAB +7, STR +2, Wpn Focus +1, sword +1). If he rolls 1-16, he misses the opponent's AC:28. NOTE even though rolls of 15 and 16 fall within the weapon's Critical Threat range, they have 'NO EFFECT unless that roll is good enough to HIT. In this case (+11 vs AC:28), 15 and 16 are misses, for no effect. A roll of 17-20 is both a hit and a Critical Threat. A re-roll is made (with the same modifiers, +11 vs AC:28)... if the re-roll is 1-16, it's just a normal hit... if the re-roll is 17-20, it's a Critical Hit for double damage.

Note that sneak-attack damage is just ADDED to the total... it is NOT multiplied on a Critical... nor is bonus damage such as Flame Weapon.

Damage that IS multiplied on a Critical includes weapon damage (eg: the base d6 for a Rapier), STR damage, weapon plusses, Elemental damage inherent to the weapon (like the +d4 Sonic damage of an Astral Blade), Weapon Specialization bonus, etc.

Note that if your opponent's AC is so high that you can only hit him by invoking the '20 always hits' rule, then it is IMPOSSIBLE to score a Critical Hit on him... only normal hits... because there is no way to roll high enough on the (second) threat roll to confirm the hit as a Critical.