The USGS Water Science School
Rivers? Streams? Creeks? They are all names for water flowing on the Earth's surface. As far as the Water Science site is concerned, they are pretty much interchangeable. I tend to think of creeks as the smallest of the three, with streams being in the middle, and rivers being the largest.
Most of the water you see flowing in rivers comes from precipitation runoff from the land surface alongside the river. Of course, not all runoff ends up in rivers. Some of it evaporates on the journey downslope, can be diverted and used by people for their uses, and can even be lapped up by thirsty animals. Rivers flow through valleys in the landscape with ridges of higher land separating the valleys. The area of land between ridges that collects precipitation is a watershed or drainage basin. Most, but not all, precipitation that falls in a watershed runs off directly into rivers - part of it soaks into the ground to recharge groundwater aquifers, some of which can then seep back into riverbeds.
A river is nothing more than surface water finding its way over land from a higher altitude to a lower altitude, all due to gravity. When rain falls on the land, it either seeps into the ground or becomes runoff, which flows downhill into rivers and lakes, on its journey towards the seas. In most landscapes the land is not perfectly flat -- it slopes downhill in some direction. Flowing water finds its way downhill initially as small creeks. As small creeks flow downhill they merge to form larger streams and rivers. Rivers eventually end up flowing into the oceans. If water flows to a place that is surrounded by higher land on all sides, a lake will form. If people have built a dam to hinder a river's flow, the lake that forms is a reservoir.
Major rivers of the world.
The water in a river doesn't all come from surface runoff. Rain falling on the land also seeps into the Earth to form ground water. At a certain depth below the land surface, called the water table, the ground becomes saturated with water. If a river bank happens to cut into this saturated layer, as most rivers do, then water will seep out of the ground into the river. Groundwater seepage can sometimes be seen when a road is built through water-bearing layers, and even on a driveway!
Look at the diagram below. The ground below the water table, the aquifer (the purple area), is saturated, whereas the ground above (the pink area) is not. The top layer (unsaturated soil/rock material) is usually wet, but not totally saturated. Saturated, water-bearing materials often exist in horizontal layers beneath the land surface. Since rivers, in time, may cut vertically into the ground as they flow (as the river cuts into the purple section in the diagram), the water-bearing layers of rock can become exposed on the river banks. Thus, some of the water in rivers is attributed to flow coming out of the banks. This is why even during droughts there is usually some water in streams.
The phrase "river of life" is not just a random set of words. Rivers have been essential not only to humans, but to all life on earth, ever since life began. Plants and animals grow and congregate around rivers simply because water is so essential to all life. It might seem that rivers happen to run through many cities in the world, but it is not that the rivers go through the city, rather, the city was built and grew up around the river. For humans, rivers are diverted for flood control, irrigation, power generation, municipal uses, and even waste disposal. And, if you ask any of these people recreating on the Chattahoochee River in Atlanta, Georgia what the best use of a river is, they might just say "to have fun."
To get a better perspective of the relative importance of large and small rivers in maintaining continental water balance, consider some statistics on the amounts of water that flow or discharge out of rivers. The Mississippi, North America's largest river, has a drainage area of 1,243,000 square miles (about 40 percent of the total area of the 48 conterminous states) and discharges at an average rate of 620,000 cubic feet per second. This amounts to some 133 cubic miles per year and about 34 percent of the total discharge from all rivers of the United States. The Columbia, nearest competitor of the Mississippi, discharges less than 75 cubic miles per year. Relatively speaking, the great Colorado River is a watery dwarf, discharging only about 5 cubic miles annually. On the other hand, the Amazon, the largest river in the world, is nearly 10 times the size of the Mississippi, discharging about 4 cubic miles each day or some 1,300 cubic miles per year -- about 3 times the flow of all U.S. rivers. Africa's great Congo River, with a discharge of about 340 cubic miles per year, is the world's second largest. The estimated annual discharge of all African rivers is about 510 cubic miles. It has been estimated that the total amount of water physically present in stream channels throughout the world at a given moment is about 500 cubic miles, The estimated total discharge from all rivers, large and small, measured and unmeasured, is about 8,430 cubic miles yearly (about 23 cubic miles daily). The estimated total discharge from all rivers about 23 cubic miles daily, with about 4 cubic miles coming from the Amazon River and about 1 cubic mile from the Congo River in Africa. (EPA). (http://www.epa.gov/safewater/kids/wsb/pdfs/The%20Water%20Sourcebooks%20-%20Grade%20Level%209-12.pdf)
Investigate the Water Cycle: Streamflow (in many languages!)