What is a Lathe?

"A lathe is a machine tool which rotates the workpiece on its axis to perform various operations such as cutting, sanding, knurling, drilling, or deformation with tools that are applied to the workpiece to create an object which has symmetry about an axis of rotation." -wikipedia

Basic Lathe A metalworking lathe from 1911 showing component parts
a = bed b = carriage (with cross-slide and toolpost) c = headstock d = back gear (other geartrain nearby below drives leadscrew) e = cone pulley for belt drive from an external power source f = faceplate mounted on spindle g = tailstock h = leadscrew

Taig Micro Lathe Overview:

The Taig functions very much the same as larger lathes, but within a smaller envelope and without the direct threading option (note: you can still thread on a Taig but it requires taps or dies).

Taig Lathe Image