Coordinate Reference Systems
An integral part of all spatial data is the coordinate reference system (CRS), which is used to define meaningful distances between data points irrespective of their values. Distances become meaningful as soon as the origin of a particular reference system and its units are known. The origin of a CRS may lie at Earth’s gravity center or at some other arbitrarily defined location. The units of a CRS can be meters, kilometers, degrees or some other arbitrarily defined variables.
In practice, a CRS is used to represent vector or raster data in some geographical space, e.g. on Earth. Unfortunately, Earth is 3-dimensional (at least) and most media for representing space is 2-dimensional or planar (like paper and computer screens). This causes a lot of trouble because it makes a 3D to 2D transformation or projection necessary.
Geographic CRS
A geographic CRS is used to identify any location on Earth with two coordinates, namely latitude and longitude. Latitude describes the angular distance from the Equatorial plane based on a 3-dimensional spherical or ellipsoidal model of the Earth. Longitude describes the angular distance from the Prime Meridian plane in Greenwich, UK. A projected CRS is based on calculated 2-dimensional Cartesian coordinates, which are linked to real 3-dimensional locations on Earth by a mathematical model.
CRSs and projections in R
CRSs and projections can be defined in R by an epsg code or by a proj4string character string. Note that proj4 is depricated and the transition to the new proj6, proj7 or WKT standards currently causes a lot of trouble.
More information
For more detailed (and better) information see www.rspatial.org and Geocomputation with R