There are a few times that we see Luke say this in the book of Acts, that the word of God was spreading across an area. Following the initial “explosion” onto the scene, when Peter preached and 3,000 people believed, the church had been growing on a daily basis.
But Luke specifically notes here in Acts 6 that the word of God was spreading:
So the word of God spread. The number of disciples in Jerusalem increased rapidly, and a large number of priests became obedient to the faith.
Acts 6:7
The apostles had faced a situation in which some of the Greek-background widows were being overlooked in the distribution of foods. They considered how they could be involved, but decided that it would be best if they continued to lead prayer and the “ministering of the word”, essentially meaning the teaching and preaching of God’s word.
It wasn’t as if these other men who were chosen to manage the food distribution were second-rate guys. Instead, the qualifications were that they were men known to be full of the Spirit and wisdom. There were seven that they chose and they became the first deacons, responsible to manage some of the physical work of the church.
We can even see that Stephen, one of the seven that was chosen, was targeted by the Jews of one of the synagogues because he had been performing signs and was proficient in speaking about his faith. So he wasn’t limited by any means in what he was being asked to do. His “ministry” wasn’t just to give food to the widows. Stephen was working also in speaking and preaching the word of God. He was also performing signs and wonders to confirm the words that he was preaching. Stephen was not only a man who was at work in the physical ministry but also at work in telling others about Christ.
But it was immediately after this division of labor and the caring for the issues of the business of the church while not neglecting the word that Luke notes that the word of God was continuing to spread. Bringing more workers into the fold allowed God to use each of the individuals for the greater purpose that He was unfolding in their midst.