The motherboard is the guts of any modern PC: it is a large circuit board into which all the other components either slot or are connected via cables. The motherboard defines which Processor Family can be used, the type and how much RAM -as well as the type and number of Drives that can be attached.
The motherboard is .. a large circuit board into which all the other components either slot or are connected via cables
The motherboard size will also dictate which Cases that can be used; although most will accommodate the main motherboard sizes (-aka form factors) that are currently widely available, you should always check those supported by the case prior to purchasing. Currently, the most popular form factors are:
Motherboards are specific to a Processor Manufacturer (-i.e. Intel or AMD) and will have a socket suitable for one or more of that company's processors.
The photo below shows a typical motherboard (-this is a mini-ITX board with the processor/fan built in):
As with processors, there are a lot of different motherboards out there! Which one you choose depends mainly on the following (-in order of importance):
Beware that both Intel and AMD use multiple sockets and only a subset of their processors will fit each
Which processor you are planning to use: this needs to be compatible with the socket on the motherboard - for example socket AM2 / AM3 (AMD) or Socket 778 (Intel). Beware that both Intel and AMD use multiple sockets and only a subset of their processors will fit each
What resources you need:
The maximum amount of RAM supported: different motherboards will have a different number of memory slots
The maximum amount of Drives supported: different motherboards will have a different number of SATA and/or IDE ports available to connect to devices such as CD/DVD burners, hard drives and SSDs
Any other requirements - such as build in graphics or sound support
Price: the more facilities and cutting edge features that the motherboard supports, the costlier it will be
Manufacturer: with motherboards, it's best to stick with a well known manufacturer (-examples include Asus, Gigabyte, ASRock): I find it useful to use a search engine to see what other people think about a motherboard manufacturer if they are an unknown quantity