Lightning strikes deposit somewhere on the order of a few Mega-Joules, not enough to power a flux capacitor, but it seems that the peak power of a bolt is about 1 terrawatt, a thousand times too large; you'd fry the delorean with that sort of energy.
It appears that 1.21 Gigawatts is roughly the energy of a nuclear power unit, though this sort of unit would be made of several rods, many more than those that fuel the Flux Capacitor.
Unless we find the dubious science correspondent referred to by the directors in the commentary (the one who pronounced it Jigowatt) we'll never know if they advised this number or it was plucked out for 'sounding nice'.
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It is a large number, one which defies non-nuclear methods of portable generation (even to this day).
The number has some appeal visually, and could be spoken memorably by the actors involved.
It perfectly fit the story purposes, and is not outside of the bounds for a lightning strike, as Pureferret says.
A number low in the gigawatt range was exactly what was needed, and Doc Brown was equal parts crazy and brilliant - he would have calculated how much power is needed, and would also use the exact number (1.21) instead of rounding it as most people would.
Thus, 'one point twenty-one' - it's a good number to speak, it doesn't have too many syllables.
Most likely, one of the writers picked it at random (possibly along with several others) and the writers decided it fit best.
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Bob Gale (the film's creator) spoke to this in a recent interview.
In short, the number "sounded good" and was evidently based on a brief conversation he had with an electrical engineer working as a consultant for the film about the amount of energy contained in a bolt of lightning.
MTV: OK, let's geek out for a minute.
1.21 giggawats.
Why 1.21?
Whynot 1.22 or 2.21?
Gale:
We did some research, and I think it's relatively accurate.
1.21sounded good.
It is like, why 88 miles per hour?
It's easy toremember.
As a writer, you want to find the words that'll sound rightso it'll be stuck in the audience's mind.
The electrical engineer wespoke with about how much electricity is in a lightning bolt, hepronounced it jig-a-watt.
We'd never heard the term before.
You cancall it gig-a-watt or jig-a-watt.
They're both correct.
I actuallymisspelled it in the script, and spelled it jigowatt.
That's why Docand Marty pronounce it that way. ' BACK TO THE FUTURE'
CREATOR BOB GALE ON EASTER EGGS, ERIC STOLTZ, SEQUELS AND THE 25TH ANNIVERSARY
( transcription errors corrected by me )
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There's nothing magical about this particular number, it's just a lot of watts.
Note that the actual unit is "gigawatts," but the producers didn't how to pronounce it, so it became “jigowatts” in the movie.
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To answer your direct questions its a MacGuffin just something to advance the plot.
How to answer the inferred question of why the need for so much power (in this case plutonium/
Mr.
Fusion/Steam which in fact is prove of the MacGuffin) and
the speech of 88MPH is this:
The speed is required seemingly to provide a object with the forward motion need to start a time dilation (i.e why traveling in a airplane you seem to be barely moving while someone standing on the ground sees a very fast plane).
The power is a requirement to generate a temporal flux to propel the object at the cusp of a time dilatation to another point in time.
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My theory is that it's a joke combining Einstein's theory of relativity with Roman Numerals.
E=MC(squared).
M is 1,000.
C is 100.
MC is 1,100.
1,100(squared) = 1,210,000 or 1.21 million.
If the units were kilowatts, that would make it 1.21 Gigawatts.
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I asked why the  speed was 88 MPH , and it made a lot of sense.  Now I want to ask: Why does the Flux Capacitor need 1.21 jigowatts to travel in time? Is this a magic number?
In Back to the Future, why was the power required to travel in time 1.21 jigowatts?
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<time-travel><back-to-the-future>
scifi.stackexchange.com/questions/15825
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Some say that apparently, the number "sounded good" and was based on a brief conversation with an electrical engineer working as a consultant for the film about the amount of energy contained in a bolt of lightning. Another theory is that it is roughly the energy of a nuclear power unit. Others say it is most likely that one of the writers picked it at random (possibly along with several others) and the writers decided it fit best. However, there may be nothing magical about this particular number, it's just a lot of watts. The number has some appeal visually, and could be spoken memorably by the actors involved.   It provides the energy of a nuclear power unit — nothing magical.
It provides the energy of a nuclear power unit — nothing magical.