An even more common hypothesis test is the independent samples t-test. You would use this to check the equality of two samples' means. Concretely, an example of using this test would be if you have an experiment where you are testing to see if a new drug lowers blood pressure. You would give one group a placebo and the other group the real medication. If the mean improvement in blood pressure was significantly greater than the improvement with the placebo, you might infer that the blood pressure medication works. Outside of more academic uses, web companies use this test all the time to test the effectiveness of, for example, different internet ad campaigns; they expose random users to either one of two types of ads and test if one is more effective than the other. In web-business parlance, this is called an A-B test, but that's just business-ese for controlled experiment.
The term independent means that the two samples are separate, and that data from one sample doesn't...