What are map projections?
Within ArcGIS, every dataset has a coordinate system, which is used to integrate it with other geographic data layers within a common coordinate framework such as a map. Coordinate systems enable you to integrate datasets within maps as well as to perform various integrated analytical operations such as overlaying data layers from disparate sources and coordinate systems.
What is a coordinate system?
Coordinate systems enable geographic datasets to use common locations for integration. A coordinate system is a reference system used to represent the locations of geographic features, imagery, and observations such as GPS locations within a common geographic framework.
Each coordinate system is defined by:
 Its measurement framework which is either geographic (in which spherical coordinates are measured from the earth's center) or planimetric (in which the earth's coordinates are projected onto a twodimensional planar surface).
 Unit of measurement (typically feet or meters for projected coordinate systems or decimal degrees for latitude–longitude).
 The definition of the map projection for projected coordinate systems.
 Other measurement system properties such as a spheroid of reference, a datum, and projection parameters like one or more standard parallels, a central meridian, and possible shifts in the x and ydirections.
Types of coordinate systems
There are two common types of coordinate systems used in GIS:
 A global or spherical coordinate system such as latitude–longitude. These are often referred to as geographic coordinate systems.
 A projected coordinate system based on a map projection such as transverse Mercator, Albers equal area, or Robinson, all of which (along with numerous other map projection models) provide various mechanisms to project maps of the earth's spherical surface onto a twodimensional Cartesian coordinate plane. Projected coordinate systems are sometimes referred to as map projections.
For a conceptual overview, see Georeferencing and coordinate systems.
Coordinate systems (either geographic or projected) provide a framework for defining realworld locations. In ArcGIS, the coordinate system is used as the method to automatically integrate the geographic locations from different datasets into a common coordinate framework for display and analysis.
ArcGIS automatically integrates datasets whose coordinate systems are known
All geographic datasets used in ArcGIS are assumed to have a welldefined coordinate system that enables them to be located in relation to the earth's surface.
If your datasets have a welldefined coordinate system, then ArcGIS can automatically integrate your datasets with others by projecting your data on the fly into the appropriate framework—for mapping, 3D visualization, analysis, and so forth.
If your datasets do not have a spatial reference, they cannot be easily integrated. You need to define one before you can use your data effectively in ArcGIS. The spatial reference or coordinate system is metadata. It describes the coordinate framework that the data is already using.
When you define the coordinate system for a dataset using the Define Projection tool or the dataset property page, you are updating the metadata to identify the current coordinate system. The dataset's extent and coordinate values will not change. The dataset must already be using the coordinate system. To change a dataset's coordinate system, including its extent and values, use the Project or Project Raster tools.
What is a spatial reference in ArcGIS?
A spatial reference in ArcGIS is a series of parameters that define the coordinate system and other spatial properties for each dataset in the geodatabase. It is typical that all datasets for the same area (and in the same geodatabase) use a common spatial reference definition.
An ArcGIS spatial reference includes settings for:
 The coordinate system
 The coordinate precision with which coordinates are stored (often referred to as the coordinate resolution)
 Processing tolerances (such as the cluster tolerance)
 The spatial or map extent covered by the dataset (often referred to as the spatial domain)
Learning more about coordinate systems
Here is a series of links to help you learn more about applying map projections and coordinate systems in your work.
Concept 
Where to go for more information 

To understand geographic coordinate systems and latitude–longitude 

To understand projected coordinate systems 

To learn which map projections are supported 

To learn about datums 
See Datums 
To learn about spheroids and spheres 

To choose a map projection 

To learn about the geodatabase spatial reference. 
See the Geodatabase Spatial Reference. 
Common coordinate system and map projection tasks in ArcGIS
Here is a series of links to guidance on how to perform a number of common coordinate system tasks in ArcGIS.
Common task 
Where to go for more information 

To define the spatial reference for a new dataset in the geodatabase 
See An overview of spatial references in the geodatabase 
To record the coordinate system of an existing dataset 
See the "Define Projection" tool in An overview of the Projections and Transformations toolset 
To define the coordinate system for external raster and image files 

To project feature, rasters, and image data layers 
See An overview of the Projections and Transformations toolset 
To identify an unknown coordinate system 
Common task 
Where to go for more information 

To learn transformation concepts 

To transform and rubbersheet data layers 

To georeference unregistered raster data 
See Changing the geographic coordinates of a raster dataset: georeferencing 
To georeference unregistered CAD data 
Common task 
Where to go for more information 

To learn vertical coordinate system concepts 

To define a vertical coordinate system for a feature class 
Object type 
Where to go for more information 

Geographic or vertical coordinate systems 

Projected coordinate systems 

Geographic (datum) transformations 