The most popular kind of PC is one based on an old IBM design, containing an Intel processor and running Microsoft Windows.
IBM created the design but pretty much every manufacturer and his dog have created a PC parts that fit this design. These manufacturers are called "third party vendors".
One IBM PC contains many parts, called IBM PC compatible hardware.
The base unit is the big case packed with a power supply, motherboard, disk drive and other hardware.
The scary looking PCB (Printed Circuit Board) in the middle of the base unit is called the motherboard. All the other components are either soldered onto this or are attached by cables. The way things are stuck onto a motherboard is called the form factor. Form factors have catchy names like AT, ATX and BTX.
The processor in an IBM PC is an Intel x86. This is actually a category that covers processors named 80386, 80486 and Pentium. These all contain 32 bit-wide channels for squirting data around. Previous processors were 16 bit and the latest ones are 64 bit.
The Intel organization has been banging out processors since the paleolithic era. In 1985 Intel produced the 80386 and most of the processors they built for the next two decades are backwards compatible with this. All these processors are collectively labelled "Intel x86" or, for RSI sufferers, "i386". Other popular processors include the Dec Alpha, Sun Sparc and Motorola PowerPC.
Just to confuse things, as is normal in computerland, the type of processor in the computer is also called its architecture.
Software only works with one type of processor, so a lot of software is written to run on the Intel 80386 processor. It is then sure to run on most PCs built in the last two decades. This software is sometimes described as "for the i386 architecture".
PCI (Peripheral Component Interconnect) is a standard design for a bus. A bus is a set of electrical conductors that connect a bunch of circuits together. A base unit contains several PCI slots. Many manufacturers make PCI cards that can be inserted in these slots. Other types of bus are AGP (used for graphics cards) and ISA (the ancestor of PCI).
In 1981 IBM released model 5150 and the IBM PC was born.
So many bits of the original design have been replaced over the years (such as replacing the ISA bus with PCI, the floppy disk drive with a DVD writer and 16 bit registers with 64 bit) that you have to look real hard to find the similarities between a twenty year old PC and a current one.