The thrust to weight ratio, or TWR for short, determines the performance of a rocket and whether it is safe to fly or not. It is the average thrust of your rocket divided by the maximum weight. Below is an example of calculating TWR for an Atlas V rocket;

This means that the Atlas V has a TWR of 73.4, much higher than the average TWR of 5-10 you see in high power rockets. 

Interpreting TWR

Your TWR will determine how fast your rocket will move upwards. A TWR greater than 1 will move upwards, a TWR less than one will slowly move down (or not move off the launchpad), and a TWR of exactly 1 would in theory hover in place. 

In reality, a TWR much greater than 1 is needed for proper flight. For example, at NAR and TRA launches, a TWR of at least 5 is needed. This will ensure that the aerodynamic surfaces have enough air moving over them to ensure a stable flight.

Another use of the TWR is determining the efficiency of rocket motors. A higher TWR means that a single rocket motor can lift more of a rocket with it as it flies.