A private pilot certificate is the FAA certificate that lets you act as pilot in command of an aircraft and carry passengers, anywhere in the United States, day or night, in aircraft you are rated and current in. Pilots call it a PPL. 14 CFR 61.109 requires at least 40 hours of flight time, including 20 hours of flight training from an instructor and 10 hours of solo. 14 CFR 61.103 sets the minimum age at 17, and 14 CFR 61.23 requires at least a third-class medical certificate before you fly solo.
The FAA's 40 hours is a floor rather than a forecast. AOPA puts what students actually need at between 50 and 70 hours, and where you land in that band is decided almost entirely by how often you fly rather than by aptitude. That is why our programs are priced as fixed packages — $10,900 for 40 logged hours, $15,900 for 60 — instead of an hourly meter that charges a slow student more. Almost everyone starts the same way, with a discovery flight at Van Nuys: one hour, $229, and you fly it yourself.
What the certificate does not let you do is be paid to fly. 14 CFR 61.113 prohibits acting as pilot in command for compensation or hire, with the limited exceptions listed in that section, and permits a private pilot to pay no less than their pro rata share of a flight's operating expenses. Being paid is what the commercial certificate at 250 hours under 14 CFR 61.129 is for. The full privilege list, and the cost-sharing arithmetic people get wrong, is on our PPL pilot privileges page.