Let's pick the one they had in the article. Suppose that the "true positives" are 5% of the population, and we have 1000 people to take the test (so 50 people are positive and 950 are negative). Let's assume the test can correctly identify a "true positive" as positive 90% of the time (so 10% of the time it gives a false negative for someone that is actually positive), and it will also ID a "true negative" as negative 90% of the time (so 10% of the time it give a false positive for someone that is actually negative).

So now we test our 1,000 people. For the 50 "true positives" we get 45 positives and 5 negatives (10% false negative rate, and we correctly ID 45 of the 50 positives). Now, we test the 950 "true negatives" and we get 95 positives (10% false positive rate), and 855 negatives.

Now, overall we have 140 people test positive. So if you tested positive, you really only have a 50/140 (35.7%) chance of truly being positive. Short take away, if you are testing for something that is "rare" in a population, you need a very good test.