score:5
No.
It means that the passport should be valid for at least 6 months when you enter the country. But usually the rule is that on the day you leave the country you passport should be valid for at least another 6 months.
Upvote:2
As other answers already explained, it does not mean you have to wait before travelling but that your passport must still be valid for some time when you return. So what you need to worry about is not the beginning but the end of your passport's period of validity.
Additionally, while your quote doesn't explain it clearly, those rules typically apply only to foreign nationals. So as a US citizen, you can (re)enter the US at any time, even on your passport's last day of validity, but you might not be able to enter another country if your passport is soon to expire.
As far as the US is concerned, you can leave and reenter at any time provided you have a valid passport.
Upvote:3
If you received your brand new passport and its validity starts today, you can travel today. If your passport is valid for ten years, then some countries require a passport that remains valid for further six months after entering. So in nine years, six months, and one day from now, some countries might not allow you to enter with your passport that becomes invalid within six months.
The reason is that for whatever reason, you might stay longer than planned. Say an accident and you stay in hospital, you get arrested for punching someone, or whatever reason. With six months validity of your passport, the risk that you stay until your password is invalid is minimal. If you went on a one week holiday with a one week valid passport, even just a small damage on the airplane, or oversleeping if your flight back is in the morning, might mean that your passport is invalid by the time you leave.
BTW. The passport guide mentions six months, which some countries have, but many countries will require at least three months, so don't wait too long renewing your passport.