Objects

Object in 3D is usually a convinient way to represent a set or vertices, faces, normals, maps and other things.

OpenGL and objects

APIs, like OpenGL or DirectX generally don't have conception of the object, they "think" in terms of points. The objects are divided into polygons, which are divided into faces, which are rasterized into pixels.

The closest thing to "object" in OpenGL terms is buffer object, used to draw triangles.

However in game programming, grouping triangles, along with their vertices, normals, etc, is a good idea, so that you can optimize performance using techniques, like occlusion or frustum culling, and arranging into scene graphs.

Examples

An example of the 3D object could be a house, a tree, terrain (although often rendered as a separate entity), the player.

Usually objects are animated in some 3D application; people are usually animated via a process of skinning and bones.