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.