What are the three different parts of the backsaw?

Blade, back and handle.

The blade is the thinner steel that have teeth filed along the lower edge.

The back is the rigid steel or brass (often brass plated steel) spin that the blade is pressed into and is there to keep the blade straight and true during the cut.

The handle is usually fixed to one end of the blade by anywhere from two to six flush nuts and screws, one often specially stamped by the saw's manufacturer to display their logo and define the date of production.