It is not mentioned directly in the movie, but there is a piece of the DeLorean referred to as a "wormhole emitter" in the majority of quote-unquote "official" technical drawings/schematics/etc.
Let us assume the bright light/distortion that appears in front of the car is "the wormhole" - then it follows that the DeLorean has to drive through the wormhole; and in order to prevent random objects from following you through, it would summarily need to close within fairly short order. If the wormhole is maintained just long enough for a DeLorean to pass through it at 88 MPH, well... there you have it.
While this involves outside information, I believe it is born out in the actions of the movie. Consider the following plot points:
- In the original *Back to the Future*, Doc has a week to prepare for the Hill Valley lightning storm, and he has at least a rudimentary understanding of his own work - indeed he still has the wound from the incident that provoked the image of the flux capacitor! So we can assume that he knows his own work well enough to find an optimal solution - and in this case it involves running a time machine straight at a lightning rod. The cop that approached him during his initial setup asks for a permit for his 'weather equipment' story, which he readily produces. So, he *could* have propped the DeLorean up on a treadmill, passed it off as "highly specialized weather-sensitive equipment" and just hung out under the clock tower until 10:04 PM - but he doesn't do this, presumably because it is necessary.
- In *Back to the Future: Part II*, the DeLorean time travels while stationary. This should throw the theory out the window - but consider this:
- The flux capacitor is, presumably, *a capacitor*. Its primary task is to store energy and discharge it when needed. If 1.21 jigowatts is the nominal amount of electricity required under normal circumstances, the capacitor will release it at a preset amount. Hopefully, Doc designed it to handle the occasional, ah, hiccup - meaning it should be able to store a bit more than it is intended to release. As I'm aware, capacitors have a 'working' voltage (the safe maximum intended) and a 'max' voltage (the absolute ceiling on what it can withstand), so this follows.
- With that in mind, the DeLorean appears to eat quite a few lightning bolts while it's up there. If the width and breadth of the wormhole are bound at all to the amount of energy required to generate it (1.21JWe) and the flux capacitor is designed to discharge at a certain rate, AND we assume that Doc did his diligence in creating a capacitor with a much higher max voltage than its working voltage, you end up with a sustained emission from the wormhole emitter. Indeed - that resultant flash and explosion seems a bit more hectic than the others, doesn't it?
- The oft-contemplated '66' trail in the sky would appear to be a result of the fire trails from the wheels going out as they don't really have anything to burn besides air (and it's raining to boot). The path suggests that the car was *pulled into* the much larger wormhole, or even that the wormhole was created *around* the time machine. The fire trails have always gone where the wheels 'should have been', like water thrown from a centrifuge. So the curvature of their appearance means there was *some* force acting on the fire trails/the immediate region, even as the DeLorean left 1955.
- **TL;DR - Multiple lightning strikes + a steady discharge from the flux capacitor = much larger wormhole than intended. Hence, the DeLorean was already inside it and didn't *need* to drive in.**
- Finally, in *Back to the Future: Part III*, the idea is pretty much the same as the first movie; it's crucial to accelerate the DeLorean to 88 MPH. By now, the generation of the 1.21 jigowatts is well-established as academic; Mr. Fusion handles it. And unlike 1955 Doc - who may be off the hook as he's only just become familiar with his future self's final product - *this* Doc has had the DeLorean for who-knows-how-long, and wouldn't be trifled with a simple setback like being out of gas unless it was critical to drive the DeLorean through the wormhole. And I strongly suspect he's not willing to subject the unit to another overcharge (he got pretty lucky the first time - too much juice, damaged/destroyed flying circuits, yet he still landed it and in working order enough to be left in a cave for the better part of a century) so given their options, along with the implicit ticking clock of Mad Dog Tannen looking to shoot himself a temporal deviant, I'd wager he went with the safest option.
So -- in closing! Speed is a requirement because the 'wormhole/tachyon field/magic thingie' only stays open briefly, and so the DeLorean needs to get in and through it before it closes up. Otherwise he'd just build it into, like, a telephone booth or a refrigerator.
EDIT: Pardon my proof by Wiki, but according to the Tachyon Field Generator entry on Wikia, Bob Gale has actually christened this aspect of the car the "tachyon field generator". Wormhole emitter is apparently just a fandom colloquialism for the emitter on top of the roof of the car. Back to the Future isn't exactly stop-one for major scientific accuracy, but I would submit that the idea is more or less the same; create hole in spacetime, drive through hole in spacetime before it closes, improve parents' quality of life.
I know that the actual phrase isn't used in the movies; I do not believe there is an onscreen explanation, except that it facilitates several plot points and one of the most epic high points to a movie, like, ever.