From the Latin veritas – truth, verifiability is a term that stands for the ability of a message to be verified (proven to be true).
Verifiability was a keyword for the positivists. They’ve tried to use verifiability as a criteria to distinguish significant from insignificant claims or messages. For them[positivists] if a message is by definition verifiable (that is, if there is any proof or practice that could determine its authenticity), the message is significant. Otherwise, if it is unverifiable, it is deprived of meaning and thus – insignificant.
Positivism was highly related to the concept of verifiability. When the principle was discredited – in a rough and reductionistic manner, as positivists often say – the teaching has also vanished.