Well, that's an interesting question, but not one with an easy answer. There are many natural factors that you could point to that allowed Christianity to grow and spread - widespread use of a single language (Koine Greek), excellent routes of trade and travel, etc. but none of that really explains why Christianity was so widely embraced.
Really, I can only say it was the grace of God. The Gospel is a message of hope for anyone who knows he's sinful and knows he can't make that sinfulness go away by trying to cover it up with good deeds. There's something inside us that knows we can't stand before our Creator and hope we're "good enough." If we can have any hope at all, it's because our Creator has done whatever is necessary for us to be counted righteous before him - and what our Creator did was offer Jesus Christ as payment for the debt of sin we've buried ourselves in.
Why did so many believe that? Why do so many believe it? Only by the grace of God. I can offer no other reason!