Abarim Publications' online Biblical Greek Dictionary
The verb κρουω (krouo) means to knock. In the classics it appears in nuances that range from knocking heads together, to festively clapping hands or even tapping on an earthen vessel to examine it for cracks and such (hence an implied meaning of to test or examine). Also in the classics, and exclusively so in the New Testament, our verb means to knock on a door.
In our modern experience, a knock on a door will either stay unanswered or else result in a person from the other side opening and politely inquiring how the knocker may be helped. In Biblical times, however, all business was conducted on markets and in public spaces, and a knock on a door that was obviously closed for a reason was essentially a challenge to the decorum and judgement of the person inside.
In Rome, there was a small but important temple dedicated to Janus Quirinus, whose doors would be open in times of war and closed in times of peace. When Jesus said: knock, and "it" will open (Matthew 7:7-8), he also warned for the terrible war with Rome that would result in the destruction of Jerusalem and the temple of YHWH in 70 AD.
Our verb is used 9 times in the New Testament; see full concordance.