Step 1 - Defining Half-Life
In radioactive decay, as well as in other physical or chemical processes, half-life is defined as the time it takes for an initial amount to decrease in half.
If, for example, we have a sample of Uranium, a radioactive material, of 100g, we could measure the time it takes to decrease to 50g by radioactive decay. This would be Uranium half-life. The half-life is constant for each given substance. Therefore, for the Uranium to decrease from 50g to 25g it would be necessary exactly the same amount of time as to decrease from 100g to 50g.
Step 2 - Interpreting the graph
Since we know that the half-life is the amount of time that is necessary for the initial sample to decrease in half, we can look in the graphic for the time when 100% of the substance becomes 50%.
We can see that, after 1 year (horizontal axis), the radioactive remaning is 50¨% (vertical axis), i.e., exactly a half of the initial amount. The half-life of this substance will be thus 1 year.