Trust me, my eyes have been bleeding non-stop for quite some time now....
Genera is the plural for genus. A torus is basically a doughnut--an n-holed torus is a doughnut with n holes. The capitalized real stands for the Real plane--as in all of its members are the Real numbers (as opposed to, say, the Complex/Imaginery numbers). The Real plane is basically the x-y set of axes used in algebra. The bit about lines and spheres is hard to explain (suffice it to say, no, lines are not spheres bunched up together, they are lines). This is a good place to start, but without the ability to draw stuff for you, the explanation probably wouldn't fit in one journal response.
Oh, and the capitalization of Real and Complex is something I do to keep things straight--most people don't capitalize them. *shrug*
Gotcha. n, in the case of an n-torus just means the number of holes: 0, 1, 2, 3, ... n. The stuff about genus and lines/cubics is from topology and algebraic geometry; pretty awesome stuff, but lacking a little in the 'easily explained' department. Of course, linking to Wikipedia entries probably doesn't help, but it's the best I've got on short notice.
that likes to do doodly doodling!
<3