Example: If we observe an apple falling to the ground with the same acceleration many times we will try to generalize this observation and create a theory that explains this phenomenon and similar ones (such as Newton's laws and his theory of gravity). Unfortunately we can never prove such a theory in the mathematical sense since we can never be sure that the next time we perform a given experiment it will still yield the same result (it could be that the laws of physics change over time or work differently in other parts of the universe). However, we can easily falsify a given theory if we can produce even one single observation where the theory does not fit reality (which is precisely why general relativity was needed to replace the classical theory of gravity, which could not explain all experimental data [actually the new theory came even before the data in that case, which is amazing in itself]). So, in a sense, proving that something is not true is the only thing we can do with absolute certainty.
That said, theories that are proven wrong by experiment and replaced by other theories are still valid in their domain of applicability, so to say as an approxomation of the larger theory.