In ArcMap, the map window is called the Data Frame, which is where GIS datasets are symbolized and labeled within a layer-based map display. Each data frame has a particular extent representing part of the world. Hence, each data frame has a coordinate system for the map display.
By default the data frame's coordinate system is set to the first layer added to your map. So most of the time, the map's coordinate system is the same as the coordinate system of your geographic data.
However, many maps must use a specialized map projection in order to meet a particular requirement. Choosing an appropriate coordinate system for your map is often an important step to create a map display that will meet your needs.
Considerations for choosing the coordinate system
Various coordinate systems are designed to maintain certain properties, and you can often choose the coordinate system of your map and its purpose because of these properties. Here is a short overview of some key considerations.
Maps constructed for a special purpose should use a map projection that preserves important projection characteristics. For example, navigation maps often use the Mercator projection because this projection has the special property of representing a path of constant bearing as a straight line (called a rhumb line). Thematic maps that symbolize an attribute of an area, such as population density, often use a equal-area projection. And so on.
The area covered by your map will affect your selection of map projection. Several dozen map projections have been designed specifically for maps of the world, such as the Winkel-Tripel and Robinson projections. Maps of continents often use conic projections such as the Albers equal area projection.
Whether you are mapping an area with an extent longer in the east–west or north–south orientation will influence your selection of map projection. Generally, conic projections are used for areas with a greater east–west extent. Transverse cylindrical projections are commonly used for areas with a greater north–south extent.
The latitude range of your map influences the selection of a map projection. Cylindrical projections work well for mapping equatorial regions. For mid-latitudes, the map projections most often used are based on cylindrical and conic projections. Polar regions are usually mapped with planar projections.
National coordinate systems
Frequently, you create general purpose maps that cover local areas such as cities, counties, states, or provinces. Especially if these maps are to be used by government agencies, using the map projection specified by a national or regional coordinate system is a good choice. Two examples are the State Plane Coordinate System in the United States and the Great Britain National Grid for the United Kingdom. For regions not covered by a national coordinate system, the Universal Transverse Mercator system (UTM) or Gauss-Krüger (GK) is commonly used for large-scale maps. UTM zones are six degrees of longitude wide, about 660 kilometers at the equator or 330 kilometers at 60° north or south latitude.
Maps for use on the Web
Often, web maps define the coordinate system that will be used for making mashups. You'll need to match the coordinate system of the base map you choose to use, whether it is ArcGIS Online, Microsoft Bing Maps, or Google Maps. All of these online maps are stored with a continuous tiling system to support the seamless display of map data for large scale subareas (e.g., imagery and streets within a city). This requires a single map projection for the world. The spherical Mercator projection is used. This is often referred to as the Web Mercator projection.
Geographic databases are in latitude–longitude (geographic coordinates)
Many datasets and whole databases are often collected and maintained in latitude–longitude. This is especially true of organizations who build and assemble data collections that span the globe. Latitude–longitude is a spherical (geographic) coordinate system and should always be projected in your map display. Maps created with data from these systems will cover any number of objectives. Use the same considerations described above for choosing a coordinate system.