Spatial Referencing - Map Projections

Concepts
   map projection
   setting the map projection

Map projection
The map projection is the coordinate system in which an actual map is made.  In most cases, this is the same as the data projection, but not always.  Any time data layers have mixed coordinate systems, than of course the map projection will be different than at least one of the data layer's projections.

Setting the map projection
In ArcMap, the map projection is the coordinate system set for the data frame.  By default, the data frame coordinate system is the same as the first data layer added to the data frame.  This may not be what you want.  For example, if you want to show Canadian province boundaries in a regional map, the map projection will be Lambert if you start with the Canadian data, but UTM if you start with Maine data.  Portraying Maine in the Canadian Lambert projection will skew it so that North is not directly 'up' on the page.  It is easy to change this on the 'Coordinate System' tab of the data frame properties.  Here you can choose a coordinate system from a list of standard ones, or from any layer in the data frame.