Espresso lingo can be confusing. On this page I (attempt) to explain the jive of java as it relates to espresso machines.
Every espresso machine is a bit different. For simplicity, this diagram illustrates a single-reservoir steam machine. Pump machines don't always have a lid and gasket, and often come with a removable water reservoir.
Carafe: Pot with pour spout used for used for holding espresso. Typically only used with steam machines.
Filter Basket: Small metal basket for holding coffee grounds. Sometimes called a "gruppa." Fits into portafilter.
Gasket: Rubber, plastic, or latex rings that create pressure seals in machines.
Group Area: Front of machine, including group (shower) head, filter basket, portafilter, and the group handle.
Group Handle: Handle attached to portafilter.
Group Head: Metal water-diffusing filter at top of group area above filter basket.
Portafilter: Funnel shaped device, typically made of metal with one or two spouts that espresso exits through.
Pulling (a shot): The act of making a shot of espresso
Pump Handle: Handle for pumping water on a manual machine.
Reservoir: Water tank. Water is heated in the reservoir in steam machines and some pump machines.
Shower Head: See Group Head
Steam Valve: Lever or knob that allows steam to exit through Steam Wand.
Steam Wand: Metal pipe that steam can exit through in order to steam and froth milk. Can also be used for warming cups.
Any other terms that confuse you? Feel free to ask me if you have any questions.