A false negative is a result which informs someone that they do not have a disease, when in fact they do.
A false positive is a result which informs someone they do have a disease, when they don’t.
Ideally a test should never give a false negative (100% sensitivity) nor give a false positive (100% specificity). There is no known test that does this. In general, there is a trade-off going on between these two measures.