Dead Reckoning (or DR) is a method of estimating a position. It is an important part of navigation. It uses the last known point (a fix), and speed and direction the vehicle or person has moved since it was at the fix, to make a good guess where the current position is.
It is used to track where a ship or airplane or sometimes where a vehicle on land is at. Now, Global Positioning System (GPS) is used and dead reckoning is not as important. But it is still used in areas where GPS is not available or for short periods of time if a GPS update is missed. It is also good to know in case the GPS satellites are damaged by a solar flare, or equipment is lost or broken, so it is still taught to sailors and pilots.
Dead Reckoning is how the sailors mapped the world after Christopher Columbus came to the New World. Using the stars, they could find their latitude (distance between the equator and the poles). But before accurate clocks were created, they could not tell their longitude (how far east or west they were) unless they saw land that they knew. So to cross the oceans they used dead reckoning. This is also how Richard Byrd became the first person to fly to the North Pole in 1926. He was able to fly for 16 hours and come back to the place he had left, with only ice fields beneath him.