What does the statement if God did not exist then everything would be permitted imply?

The implication is that if God didn't exist, morality also doesn't exist because only God can impose moral limits on human behavior.

This is a concept often given as a reason for a deist-type belief in some sort of God, even if a person doesn't attend church, read the relevant holy text, observe the relevant holy days or rituals, etc. However, many atheists and secular humanists who reject the idea of a metaphysical deity still have a solid moral grounding. Instead of basing the moral structure upon the recorded Words of a deity (which atheists will point out are the Words of men, attributed to a deity), secular humanists base their moral structure upon the sanctity of life of each human being and a shared responsibility as a species to care for each other and the environment in which all humans live.

Actually, in most cases, if you watch a moral Christian, a moral Jew, a moral Muslim, a moral Buddhist and a moral atheist working side by side you probably wouldn't be able to differentiate between them if they were of the same ethnicity/race (ie, Caucasian, African, Asian, etc.).

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AnswerThe question, as given, doesn't make sense for the simple reason that God is the only thing whose existence is necessary. Everything else, and everybody else in the world only has contingent existence - we exist because God created us and holds us in existence. By definition if God didn't existence, then nothing would exist has He is necessary existence. In other Words, the nature of God is Existence itself, that is why He gave His Name as "I Am". The only thing implied by the statement "if God did not exist then everything would be permitted." implies that the person making the statement is either a lunatic or insane, or perhaps they just don't understand what "God" is, or the what the concept of God implies.