This is pretty amazing. It means that every pair of lines in this geometry will intersect somewhere. You can model it on the surface of a sphere, which I'll talk about later. This is geometry in which, given any line and any point not on that line, there is more than one line through that point which is parallel to the given line. Anyway, here is a model for Elliptical geometry.
Points are just normal points.
Actually, it's a little trickier than that. See, there's a problem at the boundary of the hemisphere. You have to include only half of the boundary, because you don't want lines to intersect in two different points, and if you included the whole boundary, some would. So that's Elliptical geometry. Here's a model for Hyperbolic geometry.