(1) abstract geometry; (2) storing geographic data in projected coordinates; (3) a generic ESRI term for vector features; a class for "geometry" objects.
(1) "The measures and properties of points, lines, and surfaces. In a GIS, geometry is used to represent the spatial component of geographic features."
http://en.wikipedia.org/wiki/Geometry
(2) The difference between "geometry" and "geography" data storage types: What is the Difference between Geometric and Geographic columns?
(3) The ESRI "geometry" class: http://resources.esri.com/help/9.3/arcgisserver/apis/javascript/arcgis/help/jsapi_start.htm#jsapi/geometry.htm.
