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 man has built a dam to hinder a river's flow, the lake that forms is a reservoir.

Where does the water come from?

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. Ground-water 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 earth below the water table, the aquifer (the purple area), is saturated, whereas the earth 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.

Information provided by: http://wwwga.usgs.gov