The level set method, introduced by Osher and Sethian, is a generic framework for curve evolution in N dimensions. Within this framework, a N-D curve is represented by a (N + 1)-D surface, as shown on the following picture:
In the context of image processing, one of the most important advantage of such a implict representation is that any topological change, i.e. merging and splitting of the curve, is handled automatically. The level set method also permits to generalize many active contours algorithms by offering a continuous description of a curve boundary.
For more general information about the level set method, the following Wikipedia links are good place to start:
A local linear model for level set segmentation
At Synchromedia, we introduced a local linear model for level set segmentation which allows for the segmentation of statially varying regions. The following images illustrate the evolution of an active contour that is used to segment the lungs on a CT image from The Visible Human Project: