It's typically a square ceramic package plugged into the motherboard, with a large heat sink on top (and often a fan on top of that heat sink).
All instructions the computer will process are processed by the CPU. There are many "CPU architectures", each of which has its own characteristics and trade-offs. The dominant CPU architectures used in personal computing are x86 and PowerPC. x86 is easily the most popular processor for this class of machine (the dominant manufacturers of x86 CPUs are Intel and AMD). The other architectures are used, for istance, in workstations, servers or embedded systems CPUs contain a small amount of static RAM (SRAM) called a cache. Some processors have two or three levels of cache, containing as much as several megabytes of memory.
Some of the new processors made by Intel and AMD are Dual core. The Intel designation for dual core are "Pentium D", "Core Duo" and "Core 2 Duo" while AMD has its "X2" series and "FX-6x".
The core is where the data is processed and turned into commands directed at the rest of the computer. Having two cores increases the data flow into the processor and the command flow out of the processor potentially doubling the processing power, but the increased performance is only visible with multithreaded applications and heavy multitasking.
Hyper Threading is a technology that uses one core but adds a virtual processor to an additional thread at the same time.
Normally the processor carries out one task and then proceeds onto the next task. But with Hyper Threading the processor continually switches in-between each task as if to do them at the same time.
For more information, consult the Wikipedia article on microprocessors.
Most modern computers have an "ATX form factor" case in which ATX-compatible power supplies, Mainboards and Drives can be mounted.
The Mini-ITX is much different in important ways unlike its relatives the Micro-ATX and the Flex-ATX. The mainboard size can be up to 170mm x 170 mm which is smaller than the Flex and Micro-ATX can be. Usually at less than 100 watts, the Mini-ITX PSU is energy efficient. The Mini-ITX is also backward-compatible with the Flex/Micro-ATX models.
During the 1980's and 1990's almost all cases were beige, even Apple's Macintosh line. A few rare exceptions to this were black. Only recently have computer case designers realized that there was a worthwhile market for other colors and designs. This has led to all sorts of modifications to the basic design of a computer case. Now it is easy to find cases with transparent windows and glowing lights illuminating their insides.
All computers have some sort of power supply. This converts the supply voltage (AC 110 or 220V) to different voltages such as DC 5V, 12V and 3.3V. These are needed inside the computer system by nearly every component inside the computer.
There will be a bunch of connectors coming off of the supply, called Molex connectors. They come in varying sizes, meant for different applications, such as the motherboard (usually the largest of the connectors), the hard and optical drives (a bunch of medium-sized connectors), as well as the floppy drive (a relatively small connector, also saw usage among videocards in 2004). As newer standards come out, the types of connectors have changed. Many power supplies now come with power connectors for Serial ATA hard drives. These are smaller and are "hot-swappable", meaning they can be removed and plugged in again without fear of data loss or electrical problems.
The power supply also has an exhaust fan that is responsible for cooling the power supply, as well as providing a hot air exhaust for the entire case. Some power supplies have two fans to promote this effect.
It is important to buy a power supply that can accommodate all of the components involved. Some may argue that it is the most important part of a computer, and therefore it is worth spending the money to get a decent one.