The answer include two views; one from a Christian perspective and another from Muslims perspective. Both are given below.
Islam became influencial only after Muhammad got men to fight for him. Pure preaching of Muhammad did not influence much people as he could not prove his credibility by miracles (Surah 29:50). Most people knew that the revelations Muhammad claimed are from Jewish and Christian Scriptures and from old fables they heard before ( 8:31, 16:24, 23:83, 25:5, etc..). This did not win him much followers. Later, when he had followers who believed that if they fight for Muhammad they will get wealthy from the booty and can have many women as they like. And if they get killed in the war they will be in paradise with virgins. This attracted lot of men and later by sword Muhammad was able to convert many people.
Islam was; and still; influential because of its logic, simple terms, authenticity. People believed that Quran is a text that is impossible to be written by Human because of its miraculous Arabic structure and because they are convinced with Muhammad honesty and trustfulness. Refer to related question below on Quran divinity proofs.
Hints on above Christian view:- The saying that Islam became influential only when prophet Muhammad got men to fight is false; especially for two reasons:
- prophet Muhammad; when was In Medina; was attacked by the non Muslims. The battle included around 300 Muslims with less military provisions against more than 1000 non Muslims with much more provisions. Muslims won the war. Muslims were attacked by non Muslims, during prophet Muhammad preaching; many times while they were minority and they defeated the attacks. This was because of their strong belief in the authenticity of Islam.The major miracle of Prophet Muhammad (PBUH) was the Quran that challenged all people that they never can write one verse of it on their own. This is the best miracle because it is still valid till now. you can read about the scientific miracle of Quran to know some about it. You can know about many scientific statement in Quran that their validity had been just proved by present technologies and advances in science research. Other miracles of other prophets were witnessed only by people at that time and anyone may deny them now so far he/she didn't witness them by themselves.
- Credibility of prophet Muhammad was well established before and after revelation of Quran to him. He was know as the trustful and the honest.
- How the revelations of Quran were from Christian and Jewish books and in the meantime corrects for the false beliefs in these books and corrects for their claims that Jesus is son of God or God himself. It also predicts many events that happened afterward and never mentioned in the Bible or the Torah.
- Muslims know that the 2nd eternal life is physically different than this life and that all what is mentioned in describing the Heavens (or the Paradise) are just to visualize the prosperity that they will live in but surely not physically as described. So, it is not a matter of virgins!!!
- Do you think that one fourth of the world population who are Muslims are so fooled to follow a false religion or false prophet.
Refer to related questions below.