How does early rotation increase the likelihood of a tail strike at take off?
When preparing for a flight, pilots will calculate many things, including their rotation speed. This is the speed in their takeoff roll at which they will start to pitch up, and hopefully the plane lifts off the ground. The rotation speed is dependent on many things such as temperature, altitude, and aircraft weight.

My answer here discusses the lift calculations in relation to rotation. That question covered the importance of speed related to weight. More speed is needed to create the lift to take off with a higher weight.

When the airplane rotates, it increases the angle of attack of the wing, which increases the lift coefficient (if the wing does not stall). The pilots will pitch up at a certain rate, and they do not stop until they reach a climbout attitude higher than what is possible when the main gear is still on the ground (though this may depend on company policy). They count on the plane acheiving enough lift during rotation to leave the ground so that they pass that maximum pitch while in the air.

If pilots underestimate their weight, they will calculate a lower speed than is necessary to provide the lift for takeoff. This means that when they rotate, the plane doesn't have enough airspeed yet to create enough lift to take off. So instead of leaving the ground before fully pitching up, the tail strikes the runway.

It may seem like an easy mistake to make, but thousands of pilots do it every day without a problem.