Azimuthal projections are projections that are radially symmetric in all directions from the center point of the map, which can be thought of as being the tangent point on a globe from which projection takes place.
Some azimuthal projections are in fact perspective projections, which can be constructed by following straight lines from some common origin from each point on the globe to be mapped to a flat plane tangent at that the center of the projection. The Gnomonic, Stereographic, and Orthographic projections are in this category, while the Azimuthal Equidistant projection, and Lambert's Azimuthal Equal-Area Projection are not.