Because Triangle can read and refine its own triangulations, all input and output files have iteration numbers. For instance, Triangle might read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the triangulation, and output the files mesh.4.node, mesh.4.ele, and mesh.4.poly. Files with no iteration number are treated as if their iteration number is zero; hence, Triangle might read the file points.node, triangulate it, and produce the files points.1.node and points.1.ele.
Iteration numbers allow you to create a sequence of successively finer meshes suitable for multigrid methods. They also allow you to produce a sequence of meshes using error estimate-driven mesh refinement.
If you're not using refinement or quality meshing, and you don't like iteration numbers, use the -I switch to disable them. This switch will also disable output of .node and .poly files to prevent your input files from being overwritten. (If the input is a .poly file that contains its own vertices, rather than referring to a separate .node file, then a .node file will be written.)