A lathe is used for multiple woodworking and metalworking applications such as sanding, drilling, and cutting. More than likely, a lathe will be composed of a stand, a bed, headstock, tailstock, spindle, carriage, crossslide.
Parts
*Stand/Legs or Tabletop: Many lathes will sit on top of a desk or workplace but some of the bigger ones, probably metalworking, will have their own stand or legs.
*Bed: The bed is the underbelly of the beast. All of the major working components will sit atop of it.
*Headstock: This piece will often contain most of the controls and a big spindle.
*Tailstock: This piece is set so that the wood or metal being worked on can fit between it and the headstock. It also will normally have a spindle.
*Spindle: Just as with many other machines the spindle is the rotating piece of the lathe. There may be more than one depending on your lathe model but the main one usually rests by the headstock.
*Carriage: The carriage is the main piece that holds the cross-slide and has the toolpost. It sits on the bed between the spindles.
*Crossslide is for metalworking lathes. It is used to adjust the depth of the cut. A banjo does the same thing but for woodworking lathes.
*Toolpost: The toolpost actually holds the toolbit you're working with to cut, drill or sand.
Accessories
*Chuck System: There are normally 3jaw chucks. These are good for gripping and accuracy. It's a type of clamp that can be connected to the lathe.
*Spindle Adapter: These are little pieces to ensure that you get a proper fit when you put your spindle on the headstock or tailstock.
*Live or Dead Center: So what makes a center live or dead? It sure isn't its go-gettum' party attitude. The difference, really, is that a live center can rotate freely along with the lathe because of a ball bearing whereas a dead center cannot and may require lubrication. These both hold the workpiece in place.
*Drive Center: This is pretty similar to a dead center but it has teeth.
*Face Plate: The faceplate connects to the spindle and the lathe workpiece. They can be replaced with chuck jaws.