The idea of the bisection method is based on the fact that a function will change sign when it passes through zero. By evaluating the function at the middle of an interval and replacing whichever limit has the same sign, the bisection method can halve the size of the interval in each iteration and eventually find the root.
When an interval contains a root, the bisection method is the one that will not fail. However, it is among the slowest. When an interval contains more than one root, the bisection method can find one of them. When an interval contains a singularity, the bisection method converges to that singularity.