A false negative test occurs when a diagnostic test fails to detect an illness in a person who actually is sick. In other words, you test negative for a condition when you actually should be testing positive.
False negative tests can make it difficult for doctors to treat a condition by making it hard to diagnose. A false negative on an STD test, for example, could also give people a false sense of security about the risk of passing on a disease.
When designing a diagnostic test, scientists try to balance the problem of false positives with the problem of false negatives to create the best situation for any particular disease. For example, if early treatment is really important, but the treatment is not terribly dangerous, it's better to have a test that's more sensitive and less specific. That way more people who need treatment will get it and if a few too many people get treated it's not a big deal.
However, sometimes doctors are worried that getting an incorrect positive test is more dangerous than not being diagnosed with a disease. That could be because the disease in question is relatively mild, because stigma associated with the condition is awful, or because treatment is dangerous enough that it shouldn't be used unless absolutely necessary. In such cases, tests may designed in a way that makes false negatives more common than false positives.