What does the half life of radioactive substance mean?

All radio active decay is random. In any radioactive substance each specific nucleus has a chance of decaying at one specific point in time. However we can't predict when this is going to happen. Instead we can measure the number of nuclei decaying in a given a time in the whole substance.
Using this measure which is called a count we can use a statistical model (just a fancy name for a set of equations) to predict when this count will be half of it's original value. This time is called the half life of a radio active substance. Simply put the half life of a substance is the time it takes for the count to drop by half. Using this we can calculate how long the count will take to drop to any level. A good way of doing this is using the graph of activity over time.