Rapid urban growth can contribute to environmental problems in a number of ways. Some examples include:
- It typically means that more people are living in ways that require more fossil fuels to be burned (they are driving cars more, they are using more electricity, things like that). That can contribute to global warming.
- As cities are built, farm land and forest land are destroyed and buildings built. This reduces the amount of plant life that could be taking carbon dioxide out of the atmosphere.
- Rain that falls on cities gets dirty from all the auto exhaust and other chemicals that is on the streets. It then pollutes whatever bodies of water it runs off into.
I think the previous posts are very strong and accurate. I would like to add the idea of urban sprawl as being something that can be highly damaging to the environment. As populations in cities swell and as the response to this growth is outstripped by its rapid pace, the need to expand city borders becomes a reality. This helps to destroy existent ecosystems and natural ecological balances in these areas as humans begin to live off of land that was not originally intended to host them. The disruption to animal niches as well as to natural land elements and landscapes becomes another way that rapid urban population growth contributes to environmental challenges.
I'll take the historical example of Chicago, Illinois in the late 1800s to answer this question. In 1865, at the end of the Civil War, Chicago had a population of around 90,000 people - a very big city for those days. Due to heavy industrialization, an unregulated economy and the boom of the Gilded Age, that population exploded to 900,000 by 1900.
When a city grows that fast, the growth becomes impossible to manage or regulate. You can't plan adequate sewage systems or water supplies because the population influx is faster than can be accommodated by normal government and growth systems. Such growth encourages pollution, both by business and individuals, and an overconsumption of resources without proper planning for their supply and conservation.