A false positive is when we believe something to be true which is not. A false negative is when we believe something to be untrue which is in fact true. False positives typically entail less risk and cost than false negatives. 

When our ancestors on the Savannah believed the sound in the grass was from a predator (which it was not) and ran away, they were perhaps slightly inconvenienced but otherwise  unharmed. 

If they thought the sound was just the wind (when it was in fact a predator) they quite possibly paid for their error with their lives.