It doesn’t, and there simply is no good reason the quoted description should claim it does. If you were fighting with two weapons while also using one or more natural attacks, you could use Two-Weapon Fighting to reduce the penalties on the two weapons when you use the two-weapon fighting option, but it wouldn’t do anything at all for the −5 penalty on secondary natural weapons. So far as I know, Multiattack is the only¹ feat that touches on that penalty, reducing it to −2. Since in this scenario you already used your primary hand and offhand for your weapon attacks, you can’t be using them for your natural attacks—you must be biting or something. And that being the case, those natural attacks don’t take any penalties from the fact that you’re using two-weapon fighting, which explicitly applies penalties to your primary attack and offhand attack. A bite or similar isn’t either of those and takes no penalty.
However, Paizo has, at times, demonstrated extreme confusion over their own² two-weapon fighting rules. Cf. the whole “flurry of blows is two-weapon fighting” fiasco, which still doesn’t make any kind of sense. This description of natural attacks is not found in D&D 3.5e, so it’s new Paizo text, but the two-weapon fighting rules are from D&D 3.5e, so it’s Paizo text referencing Wizards of the Coast text—incorrectly. Wizards of the Coast wrote a lot about how two-weapon fighting,³ and we know that they had absolutely nothing to do with natural attacks.
The only scenario in which I can imagine that Two-Weapon Fighting would directly improve one’s attack bonus with a natural attack is if you attack with a one-handed weapon, and using two-weapon fighting, attack with an “offhand” weapon that doesn’t actually use your hand, like armor spikes. Then, arguably, you might still be able to use a claw on the hand that didn’t use the one-handed weapon, and that might be considered offhand in that scenario and thus subject to the offhand attack penalty from two-weapon fighting, which the Two-Weapon Fighting feat directly improves. Problems with this abound, however: Paizo has stated that armor spikes still (somehow) use your hand, so getting to make that claw attack at all is dubious. And if that is allowed (which it would be under the actual rules they wrote, ignoring the FAQ), then IMO that is the offhand attack, and the claw isn’t. I have my doubts that this convoluted, dubious scenario is what Paizo had in mind when they wrote the description quoted in the question.
D&D 3.5e has an Improved Multiattack feat in Savage Species, which eliminates the penalty altogether, but there doesn’t seem to be a Pathfinder analogue. Honestly, Improved Multiattack was, for most characters, not worthwhile. Multiattack is a very good feat for natural-attack-based characters in both games.
Note that the two-weapon fighting rules are copied verbatim from D&D 3.5e, so it seems their problem here is misunderstanding those rules, and then not being willing to admit that after the fact.
For instance, “Rules of the Game: Two-Handed Fighting,” Part Two and Part Three, and “Rules of the Game: Unarmed Strikes,” Part Two. And, to be fair to Paizo, Wizards wrote all this because those rules are confusing—but Paizo had their chance to rewrite them when they wrote the Core Rulebook and they didn’t, so pretending after the fact that they did rewrite those rules—or that Wizards of the Coast had written something other than what they had—is nonsense.