This is an interesting verse. Jesus is saying that something very significant was happening in and during His own lifetime here on earth or at least during a segment of it. He places the beginning of this time with the time of John the Baptist. What is not clear is whether He means John’s birth or the beginning of his ministry.
I suggest to you that He is speaking of the Spiritual battle that was being fought in heaven that at the time was spilling over into the hearts of man. The kingdom of heaven was suffering violence. And men on earth were attempting to take it by force. In the coming days they would kill the King of Glory. At this same time were Satan and his Demons doing battle with Michael and the heavenly host? Listen:
The seventy returned with joy, saying, “Lord, even the demons are subject to us in Your name.” And He said to them, “I was watching Satan fall from heaven like lightning. 19 Behold, I have given you authority to tread on serpents and scorpions, and over all the power of the enemy, and nothing will injure you. Luke 10:17-19 NASB
But with this as with all teaching in scripture, there must be a right division. The disciples had been given spiritual power, and could not be harmed spiritually, but the battle on earth at that time was violent even as it was in the heavens. Violence was being done to the physical even of the apostles. If the kingdom was experiencing violence it was mostly felt here on earth.
Is this battle still being fought by men who are attempting to take the kingdom by force?
And think of it, does the fact that we lose earthly battles every day mean that the kingdom of heaven is at risk? Jesus saw Satan fall. The battle is perhaps more violent here on earth what with his fall. We still fight with the same spiritual weaponry, but there are more of us in the fight. The gospel has all but spread to every tribe and nation. Yet the enemy fights on. In fact, he will fight even more violently.
So the dragon was enraged with the woman, and went off to make war with the rest of her children, who keep the commandments of God and hold to the testimony of Jesus. Revelation 12:17 NASB
The battle will only end with the coming of Jesus back to this earth. Until then we must fight on employing all of the spiritual weapons at our disposal.
Our main offensive weapon is the word of God, the sword of the Spirit, and our faith in Him to wield it.