An amplifier in a separate case usually gets put on top of one or more speaker cabinets ([u]cabs[/u]) so it is referred to as the [u]head[/u].
An amplifier consists of two basic sections.
The [u]pre-amp[/u] supplies some boost to the signal from the guitar. It also may include one or more tone controls and built-in effects, or places to connect them to. These [u]effects loops[/u] allow external effects to be pre-set and then switched in or out with channel switches in the preamp. The [u]channels[/u] are different circuits that have different amounts of gain, or boost, and usually have separate tone controls.
The [u]power amp[/u] is the section that takes the output of the preamp (which isn't a whole lot stronger than the output of a guitar), and gives it enough power to drive the speakers.
If the speakers and the amp are all built into the same cabinet, this is called a [u]combo[/u]. A [u]half-stack[/u] is usually an amplifier head and one cab. A [u]full stack[/u] has two or more cabs.
A [u]power conditioner[/u] is connected between the amp and the AC mains (wall plug). Its purpose is to clean up the power before it gets to your rig. A power conditioner could be something as simple as a surge suppressor, or as sophisticated as an uninterruptable power supply (UPS) that can use storage batteries to keep the rig running during interruptions of the AC power.