The standard file format for 3D models meant to be 3D printed is the STL file format. STL files end with ".stl", from STereoLitography - the format was actually developed for 3D printers. STL format 3D files describe the objects through the use of wire meshes made of triangles. The video below shows the STL mesh of a model of a goose, as viewed in the Autodesk Inventor CAD program. The triangle mesh is visible as the white lines all over the goose.

STL files are an open file standard and are widely used in Computer Aided Manufacturing (CAM) and rapid prototyping. The STL file format is good for 3D printing because it describes a part's surface geometry in a way that is easily translated into layers that can be printed. Unfortunately, STL files are terrible for doing Computer Aided Design (CAD). They can be imported into CAD applications but are often difficult to change. TinkerCAD is one of the few programs that makes modifying STL files relatively simple.