The US military wants to understand the most important software on Earth (MITTechnology Review)

Depends on the details of the test. We have a 2x2 confusion matrix of test result versus real result, and the false positive rate tells us how many samples fall in one of the 4 cells of the matrix - in this case, how many are in the "test says yes" column and the "real world says no" row. This gives us a decent chance of guessing at the behaviour of the system when the "test says yes", and when the "real world says no", but we need more data to be able to say something about the behaviour of the system when the "test says no" or when the "real world says yes".

In particular, it's common to have a low false negative rate with a high false positive rate, or vice-versa, since the underlying judgement is likely to be a confidence level and a threshold; if you set the threshold low, you have very low false negative rates, but very high false positive rates, while if you set the threshold high, you get very high false negative rates, but very low false positive rates.