Representing a spherical view of the world on a flat computer monitor or print requires some manner of mapping from the 3D sphere in which the camera and viewer are embedded to 2D. The techniques used for mapping are of exactly the same type long used by map makers to project the entire globe, or portions of it, onto two dimensional maps. There is no single, unique projection for representing sections of the sphere on the globe. Instead, all projections have various attributes and limitations. There are many classes of projections used for various purposes (e.g. Mathword's Project Page), but only a few are traditionally used for panoramic imaging.
Some of the most common projections when working with Panoramic imaging are:
Spherical/ Equirectangular projection
Also called the "non projection", this is a representation of the sphere which maps longitude is mapped directly to the horizontal coordinate, and longitude is mapped to the vertical. This projection is often used for source images in panoramic viewers like PTViewer. See definition for Equirectangular Projection for more.
This is the projection most commonly used for printed panoramas with large ranges of longitude. It can be envisioned by imagining wrapping a flat piece of paper around the sphere tangent to the equator, and projecting a light out from the center of the sphere. A full range of longitude, up to 360 degrees, can be represented with a cylindrical projection, but near the poles, the images become very distorted. See Cylindrical Projection for more.
This is a fundamental projection which can be envisioned by imagining placing a flat piece of paper tangent to a sphere and projecting a light out from its center. Obviously, only a maximum of 180 degrees of longitude can be represented with this projection, and practically far less. Most non-fisheye cameras produce a nearly rectilinear image over their field of view. The Rectilinear projection is often used for prints of panoramas which cover less than ~120 degrees of longitude, since straight lines are preserved. See Rectilinear Projection for more.