A mesh consists of a set of vertices that are connected by edges. Edges connect to each other to form either three- or four-sided faces. (Chapter 4 covers this in more detail, along with how to work with each of these mesh building blocks.) When you tab into Edit mode on a mesh, you can manipulate that mesh's vertices (or edges or faces) with the same basic grab (G), rotate (R), and scale (S) tools that work on all objects, as well as the very handy extrude (E) function. These actions form the basis for 3D modeling, so much so that some modelers like to refer to themselves as vert pushers because sometimes it seems that all they do is move little points around on a screen until things look right.
Of course, modeling has more to it. You actually have a choice between two primary methodologies when it comes to modeling: