The 3 most important parts to be familiar with are:
The platform is the flat part at the tip of the shoe (the part you stand on). The box includes the stiff area around your toes. It is the hard part around your toes that provides support to your foot.
There are different widths of boxes for different widths of feet.
The vamp is the front part of the box, or the part that covers from the tips of your toes to your knuckles. The vamp is mostly referred to, to say how deep it is. This is important and should be relative to the length of your toes.
The shank is the stiff piece that supports your arch. It lies under the insole. Different shoe makers have different stiffness for their shanks.