OpenGL works in the homogeneous coordinates of three-dimensional projective geometry, so for internal calculations, all vertices are represented with four floating-point coordinates (x, y, z, w). If w is different from zero, these coordinates correspond to the Euclidean three-dimensional point (x/w, y/w, z/w). You can specify the w coordinate in OpenGL commands, but that's rarely done. If the w coordinate isn't specified, it's understood to be 1.0.
  

The standard algebraic model for Euclidean space Eⁿ is an n-dimensional real vector space Rⁿ or, equivalently, a set of real coordinates. One trouble with this model is that, algebraically, the origin is a distinguished element, whereas all the points of Eⁿ are identical. This deficiency in the vector space model was corrected early in the 19th century by removing the origin from the plane and placing it one dimension higher. Formally, that was done by introducing homogeneous coordinates. The vector space model also lacks adequate representation for Euclidean points or lines at infinity. We solve both problems here with a new model for Eⁿ employing the tools of geometric algebra. We call it the homogeneous model of Eⁿ.
  

As long as w is nonzero, the homogeneous vertex (x, y, z, w)^T corresponds to the three-dimensional point (x/w, y/w, z/w)^T. If w = 0.0, it corresponds to no Euclidean point, but rather to some idealized "point at infinity." To understand this point at infinity, consider the point (1, 2, 0, 0), and note that the sequence of points (1, 2, 0, 1), (1, 2, 0, 0.01), and (1, 2.0, 0.0, 0.0001), corresponds to the Euclidean points (1, 2), (100, 200), and (10000, 20000). This sequence represents points rapidly moving toward infinity along the line 2x = y. Thus, you can think of (1, 2, 0, 0) as the point at infinity in the direction of that line. 

Animating Rotation with Quaternion Curves by K. Shoemake, ACM SIGGRAPH 85