Least-cost analysis is based on a raster surface called a cost surface. In modeling how groups of people (or animals, or other agents) might cross terrain, the cost surface can be created by combining multiple rasters into one.  In the case of Sarah Davis, for instance, these included:

• A terrain roughness raster, accounting for surface roughness and other terrain restrictions.
• A resource-cost raster, modeling the tendency to stay near major river valleys that offered access to water and vegetation.
• A river-valley edge raster, assigning lower movement costs to the edges of those same valleys.
• An optional “existing trails” raster, modeling the presence of established travel routes.

The roughness and river-valley rasters are often derived from Digital Elevation Models (DEMs), the resource-cost raster can be developed using river data as a base, and known historic routes may inform the “existing trails” raster. The sum of these layers produces the cost surface for a study area.
Slope of the modeled path is then applied to create a cost-distance raster, which forms the basis of least-cost analysis.

Raster:
"In its simplest form, a raster consists of a matrix of cells (or pixels) organized into rows and columns (or a grid) where each cell contains a value representing information, such as temperature. Rasters are digital aerial photographs, imagery from satellites, digital pictures, or even scanned maps." (ESRI)

Least-cost Path: The least-cost path travels from a destination to a source (e.g., between nodes of interest). This path is one cell wide and represents the lowest relative travel cost according to the cost units defined in the original cost surface.  (ESRI) 

Least-cost corridor:
To create a corridor, two accumulative cost rasters must be generated—one for each node. The Corridor tool then adds the two accumulative costs together, producing a raster of combined travel costs between the sources.
For example, the least accumulative cost to reach node D plus the least accumulative cost to reach node E equals the total cost of a path passing through a cell. Cells below a chosen threshold value form a swath or corridor of possible travel rather than a single least-cost path. This output can be viewed as a least-cost corridor of cells instead of one narrow line. (ESRI).