Watersheds are a term commonly referred to in image processing. Gray level images are considered as topographic water reliefs, where each relief is flooded from its minima. When two lakes merge, a dam is built. The set of all dams that result are what is known as an image's watershed
A grey-level image may be seen as a topographic water relief, where the grey level of a pixel in the image is interpreted as the height within the relief. A drop of water falling on a topographic relief flows along a path to finally reach a local minimum. The watershed of a relief corresponds to the limits of the nearby catchment basins of the drops of water.
In image processing, different types of watershed lines may be computed. There are also many different algorithms to compute watersheds. Watershed algorithm is used in image processing primarily for image segmentation purposes.
Below is a visualization of the MRI of a heart visualized in a topographical way.
http://upload.wikimedia.org/wikipedia/commons/d/db/Relief_of_gradient_of_heart_MRI.png
Source: Wikipedia
These roughly correspond to the edge strength of the image, and the gradient of the image is shown below.
http://upload.wikimedia.org/wikipedia/commons/e/ea/Gradient_of_MRI_heart_image.png
Source: Wikipedia
Watersheds essentially calculate the final edges that are essentially the basins of where the water collects, and an example is shown below.
http://upload.wikimedia.org/wikipedia/commons/0/0d/Watershed_of_gradient_of_MRI_heart_image.png
Source: Wikipedia
Finally, the topographical visualization of the gradient (or the watershed) is shown below. The previous image is inevitably the result that is being sought, but the output of the watershed algorithm is what is shown below.
Source: Wikipedia
For more information about the different watershed algorithms that exist, check out the following links: