A spatial reference describes where features are located in the real world. You define a spatial reference when creating a geodatabase feature dataset or stand-alone feature class. The spatial reference includes a coordinate system for x-, y-, and z-values as well as tolerance and resolution values for x-, y-, z-, and m-values.
X,y coordinates are georeferenced with a geographic or projected coordinate system. A geographic coordinate system (GCS) is defined by a datum, an angular unit of measure (usually degrees), and a prime meridian. A projected coordinate system (PCS) consists of a linear unit of measure (usually meters or feet), a map projection, the specific parameters used by the map projection, and a geographic coordinate system.
A projected or geographic coordinate system can have a vertical coordinate system as an optional property. A vertical coordinate system (VCS) georeferences z-values, most commonly used to denote elevation. A vertical coordinate system includes a geodetic or vertical datum, a linear unit of measure, an axis direction, and a vertical shift.
M, or measure, values do not have a coordinate system.
For a spatial reference that includes an unknown coordinate system (UCS), you specify a tolerance only. It is not possible to georeference a feature associated with a UCS. You cannot define a vertical coordinate system if the x,y coordinate system is unknown. If at all possible, you should not use an unknown coordinate system. Because the valid area of use and unit of measure are not known, the resolution and tolerance values may not be appropriate for the data.
The resolution represents the detail in which a feature class records the location and shape of geographic features. It is the minimum distance, in map units, that separates unique x-values and unique y-values in the feature coordinates. For example, if a spatial reference has an x,y resolution of 0.01, then x-coordinates 1.22 and 1.23 can be stored as separate coordinate values, but x-coordinates 1.222 and 1.223 are both stored as 1.22. This is illustrated in the graphic below. The final digit on the latter pair of x-coordinates is truncated because the change in value is less than the x,y resolution. The same would apply for y-coordinates.
Software engineers like to think about integer coordinates represented on a Cartesian grid with a very fine mesh. The spacing of the mesh is defined by the coordinate resolution. All feature coordinates are georeferenced according to the chosen coordinate system and snapped to the coordinate grid. This grid, known as the coordinate resolution grid, is defined by the resolution which determines the precision (the number of significant digits) of your coordinate values. The resolution establishes the fineness of the coordinate resolution grid that covers the extent of your feature class or feature dataset. All coordinates snap to this grid, and the resolution defines how far apart the individual lines of the grid are.
Resolution values are in the same units as the associated coordinate system. For example, if a spatial reference is using a projected coordinate system with units of meters, the resolution value is defined in meters. The default resolution value is 0.0001 meters (1/10 millimeters) or its equivalent in map units. For example, if a feature class is stored in state plane feet, the default precision will be 0.0003281 feet (0.003937 inches). If coordinates are in latitude-longitude, the default resolution is 0.000000001 degrees.
Feature coordinates with smaller (finer) x,y resolutions can have more digits of precision. However, x,y resolutions that are extremely small may impact performance in terms of excessive disk use and increased I/O. As the x,y resolution value is increased (becomes more coarse), the precision associated with feature coordinates diminishes; feature boundaries will be smoothed, simplified, or not shown at all.
In the following graphic, the grid with the large x,y resolution will not be able to store the polygon feature with as much precision. Conversely, the grid with the small x,y resolution will store the polygon feature using greater precision, better preserving its shape.
Esri strongly recommends using the default x,y resolution in most cases because it has proved to perform quite well and can store adequate coordinate precision for most situations.
A spatial reference also includes tolerance values. X-, y-, z-, and m-coordinates all have associated tolerance values that reflect the accuracy of the coordinate data. The tolerance value is the minimum distance between coordinates. If one coordinate is within the tolerance value of another, they are interpreted as being at the same location. This value is used in relational and topological operations when determining whether two points are close enough to be given the same coordinate value or they are far enough apart to each have their own coordinate value.
For example, in the following graphic there are two line features of equal rank in the same feature class. During topology validation, if one vertex, V2, is located within the x,y tolerance of another vertex, V1 (or viceversa), both are moved to a new location (for example, the weighted average distance between the coordinates).
The default tolerance is set to 0.001 meters or its equivalent in map units. This is 10 times the default resolution value and is recommended in most cases. You can set a custom x,y tolerance value, but it should never approach the data capture resolution, and the minimum allowable x,y tolerance value is twice the x,y resolution.
For a more in-depth overview of processing using the x,y tolerance, see Feature tolerances.