The word bootstrap is pretty common nowadays and shows up mostly as a verb. It is used frequently in the context of Internet and technology enterprises and refers to the process of getting things done, built, or advanced without much in the way of initial resources to accomplish the task.
They bootstrapped their startup into a multi-million-dollar company without any capital from outside investors.
Prior to the usage illustrated above, the word more narrowly designated starting up a computer system from a minimal set of operating instructions which would then activate more and more of the computer’s full capabilities. The Online Etymological Dictionary cites usage from 1953 that refers to a fixed set of instructions for loading a computer’s operating system, so bootstrap in this context is still a noun, metaphorically extending the utility of a physical riding boot’s loops. (The wearer tugs on the loops as an aid to pull the boots on.) By 1975 bootstrap has expanded its role to include verb — the act of starting up a computer. The more familiar shortened form of this verb is boot and it has acquired an optional accompanying particle, boot up, and a prefix, reboot. (Normally we don’t speak of booting down a computer — we just shut it off. But, in 2001: A Space Odyssey, was Dave unbooting or booting down Hal by selectively pulling out some of Hal’s banks of higher reasoning modules? He couldn’t shut down Hal altogether and have a functioning spaceship. Perhaps unique situations and contexts require unique words? :-))
So how did this robust modern usage of bootstrap evolve from a rather obscure noun which referred to the loops attached to riding boots? A quick look at bootstrap in Google’s Books Ngram Viewer shows almost no occurrences of this form until around 1940, after which point it shows a continual rise into the 21st century.
Here’s an idea to muse: Robert Heinlein published a short story in 1941 in Astounding Science Fiction called By His Bootstraps. The story explores some of the paradoxes and implications of time travel: the main character does the seemingly impossible (lift himself up by his own bootstraps) by interacting with other versions of himself through time travel. It’s an abstract, metaphoric sense of bootstrap, perhaps even recursive in the story’s context.
Given that computer geeks are a group who tend to read a lot of science fiction, could it be that the word bootstrap gained its contemporary currency from this story by Robert Heinlein? Who decided that bootstrap was the right word for a set of computer instructions? It’s also interesting to note that the impossibility of the physical act described in the phrase lift yourself by your own bootstraps (you can only jump off the ground, you cannot hoist your feet off the ground while simultaneously standing) has become modified to mean do something on your own without external help. In this case there is a literal phrase that expresses an impossible event changing its meaning into a metaphorical phrase that expresses an act of personal industry and self-sufficiency.
Word Travels 
In analog circuit design, bootstrappingis a technique in which positive feedback from the output of an amplifier is applied to an earlier point in its circuitry in order to boost one of its operating parameters. A circuit element used for such coupling may be referred to as a ‘bootstrap capacitor,’ say, or a ‘bootstrap resistor.’
The usage is of considerable antiquity (antiquity in electronics being measured in decades rather than centuries), and I recall seeing it in application notes from semiconductor manufacturers back in the early 1970s, when linear integrated circuits were coming into their own. But it’s older than that. On p.651 of my worn copy of Terman’s Electronic and Radio Engineering (McGraw-Hill, Fourth Edition, 1955), there’s a small schematic of a ‘bootstrap saw-tooth-wave generator’ that uses two tubes (valves, for readers in the UK), and employs a bootstrap configuration as a “means of obtaining a constant current for the charging of a capacitor.” In describing the operation of the circuit, Terman concludes:
Personally, I would be very surprised if the word bootstrap in a feedback context didn’t extend back into the 1940s and perhaps even earlier.
It seems to me a useful distinction between the usage I’ve described, and the process of boot(strapp)ing a computer, is that the former describes an equilibrium condition, while the latter terminates once the actual operation of the system is underway. In that sense, it might better be described as self-organization. A non-technical analogy might be the U.S. decennial census, which self-organizes in precisely the same way — it’s a contagion model, like plague spreading from its natural reservoir, its boot sector…
Interesting history from electronics on this term, BBear! It seems that the computer world could well have adapted the term from their EE cousins’ usage, rather than from a literary reference in science fiction.
I have seen similar explanations for “bootstrapping” on earlier occasions, but from the far older stories about Münchhausen.
Welcome, Michael! Thanks for the reference to the Münchhausen stories. Apparently he could pull himself up by either his own hair or his own bootstraps, according to different accounts?