An overview of the Projections toolset
This topic applies to ArcGIS for Desktop Advanced only.
The Projections toolset contains tools to set a projection for, reproject, or transform a coverage. Properly projected data ensures accurate, reproducible representations and measurements with your GIS data.
Maps are flat, but the surfaces they represent are curved. Transforming threedimensional space onto a twodimensional map is called projection. Projection formulas are mathematical expressions that convert data from a geographical location (latitude and longitude) on a sphere or spheroid to a representative location on a flat surface. The process distorts at least one of these properties—shape, area, distance, direction—and often more. Because measurements of one or more of these distorted properties are often used to make decisions, anyone who uses maps as analytic tools should know which projections distort which properties and to what extent. Briefly, conformal maps preserve shape; equal area, or equivalent, maps retain all areas at the same scale; equidistant maps maintain certain distances; and azimuthal, or true direction, maps express certain accurate directions.
Tool 
Description 

Records the coordinate system information of the Input Coverage including any associated projection parameters, such as datum and spheroid. 

Changes the coordinate system of your coverage including its datum or spheroid. 

Moves all features in a coverage based on a set of from and to control points. 