Could someone explain to me exactly what mesh modeling is? and what are some of its downfalls?

Mesh modeling means you are working on a bunch of points that when connected together, look like a real life object. There are several tools used in software packages to do this: Splines Nurbs Subdividing extruding etc..... But in it's most basic form. You place a bunch of dots in the scene then connect them to display an item. Just like in those kids connect the dots books. Only in three dimensions instead of two. Both items in the picture here are mesh models. By adding more points and connecting them together, you get a more complex result. ScottA

LOL @ScottA "Just connect the dots" If only it were that easy.