Why did towns and cities grow during and after the Industrial Revolution?

The primary answer is the employment boom that accompanied the Industrial Revolution. The factories were located in the towns and attracted the rural population with new jobs. In fact, the Industrial Revolution brought more people into the cities than ever before. For instance, in 1850 Great Britain had more people living in the cities than the countryside. This occurred later for the United States as well.
Along with the employment came wealth. As people became employed in these cities and found a little more wealth than they were used to, they settled down with homes. These homes produced children and the families began to grow. Schools were created and more businesses popped up along the way. All of this only fueled the population boom in cities around the time of the Industrial Revolution.

The Industrial Revolution created new employment opportunities for tens of thousands of people. The vast majority of this new workforce consisted of rural dwellers, who headed to the towns and cities in search for work. Inevitably, this resulted in the growth of urban areas, their populations increasing dramatically due to the influx of new arrivals. The new factories and other enterprises at the heart of the Industrial Revolution were based in the towns and cities. It was here that goods were manufactured and where most of them were sold. The rapid growth of the urban population created a growing demand for industrial output. In turn, this generated additional jobs, which led to more rural dwellers heading to the towns and cities, and so on.