Why is motherboard used to refer to the main board of a computer? What is the relationship with the word mother here?
It's called a motherboard because it is the main circuit board in the computer, and it can be extended by plugging other circuit boards into it. These extensions are called daughter boards. Wikipedia suggests that historically a "mainboard" was not extensible in this way, hence the need for different terminology. Many computer terms use human or biological words as metaphors:
The first references I found are in 1956 to "mother" board, "mother-board" and "mother board"; the quotes suggest this is new terminology.
The observant will have noticed one of these early uses of mother-board are in conjunction with baby-board, and not today's common daughterboard. A mother-baby relationship seems more appropriate in this context than mother-daughter.
Daughterboard is the most common term nowadays. When did this replace baby-board?
The earliest I found was ten years later, in 1965 as daughter board, "motherboard-daughter board" and mother-daughter board.
Mother lode and mother ship are older compounds along similar lines (both dating to at least 19th century, in mining and whaling respectively). Perhaps motherboard was coined by analogy with one of those? (Influence from mother ship seems very plausible, due to its sci-fi popularity.)
In each case, “mother X” seems to mean roughly “a big X, associated to some group of smaller X’s” — the metaphor seems fairly clear.
Unfortunately I can’t find any reliable sources right now with specific info on the origin of motherboard — hopefully someone else can, or I’ll try again tomorrow when I have OED access again…