Maps are usually seen in a flat, two-dimensional medium such as a drawing on paper or an image on a computer screen. Since the surface of the Earth is curved, or three-dimensional, the visual elements on the surface must somehow be transformed from three dimensions to two in order to display a map of the Earth's surface. Projections are a mathematical process by which the visual elements are transformed from three dimensions to two.
One of the simplest forms of projection is analogous to shining a light through a translucent globe onto a piece of paper and tracing the outlines. Other forms of projection may involve dozens of complex mathematical equations. Since no two-dimensional representation of a three-dimensional surface can be accurate in every regard, a variety of different projections have been developed to suit different purposes. Some projections are accurate in terms of area but not in scale, some are accurate in terms of scale but not in shape, and so on. The selection of an appropriate projection for a map depends on which characteristics of a map are most important or most desirable for a given project or audience.
Surfer supports several of the projections that are most often used in modern cartography and related fields. The Surfer worksheet allows you to load data and define the projection using the Data | Coordinate System | Assign Coordinate System command. You can then convert the data to another coordinate system using the Data | Coordinate System | New Projected Coordinates command to project the data in another projection, ellipsoid, or datum. Surfer's plot window allows you to assign a coordinate system to a grid file using the Grids | Edit | Assign Coordinate System command. You can also load maps, assign map coordinate systems using the Source Coordinate System for each map layer, and convert the entire map to another system using the Target Coordinate System.
There are many excellent textbooks and publications on this subject, and we do not attempt to explain projections in full detail here. If you need or want more information, you might consider reading the references that provide good introductory discussions of map projections.