Why do computers keep the correct time and date when they haven't been connected to the internet for years?

That depends on what you mean by "correct." Most personal computers have a real-time clock chip that stores the time and date, and a battery that keeps the clock running. A decent battery can run the clock for a decade or more. That said, the clock will almost always drift out of sync with "standard" time. The average real-time clock gains or loses a second per day.

Also, even without internet access, a computer can maintain the correct time if it has an accurate time source, like a GPS receiver, or there is a local NTP server on the network with one.