Learn English – Origin of the word “facebook”

It's an informal way of spelling 'to come', which can mean having an orgasm. How exactly that verb has become associated with sexual acts is unclear (to me). My best guess would be that it was commonly used in a phrase similar to:

I'm coming to an orgasm!

The word is formed (obviously) from the adjective main applied to frame, which tends to coalesce into mainframe in any context where a particular main frame becomes a standard component and needs a noun for convenient reference. For example, the term was used for the main frames of locomotives and early automobiles. A particularly relevant such use is in telephone infrastructure, where there was a large frame used for an exchange, holding wiring and relays for a group of phone lines with a common prefix. For instance, in this 1918 article, the diagram has an arrow labeled "to new exchange mainframe".

Early computers used a large frame (much larger than "racks" used now) to hold wiring and components for part of a computer (like that shown here). By the late 1950s, a typical installation might have a single large frame holding the central processing unit, to which bundles of wires from peripherals ran. To those familiar with the similar usage in telephone technology, mainframe would have been a natural usage for this CPU frame. For example, in this 1961 article, a Western Electric (of AT&T) staff member writes:

Likewise, the output of a computer mainframe is digital...

The term became more widely adopted, in particular for the large central computer used by a company as distinguished from smaller computers which began to appear in the 1960s. It is not terribly surprising that the earliest source quoted by the Oxford English Dictionary for mainframe is a 1964 glossary from Honeywell, then a producer (among other things) of smaller computers and soon minicomputers.