Hypothesis test
A hypothesis test uses sample data to weigh a null claim against an alternative, gauging how surprising the data would be if the null claim were true.
A significance test decides whether the evidence in a sample is strong enough to reject a default claim about a parameter. You state a null and an alternative hypothesis, compute a test statistic, and find its p-value under the null. For example, to test whether a coin is fair you compare the observed number of heads to what a fair coin predicts. If the p-value is at or below the significance level, you reject the null hypothesis; otherwise you fail to reject it.
More hypothesis testing terms, or browse the full statistics glossary.