We can't talk about Back to the Future without mentioning the famous DeLorean time machine: the one that goes a little nutty whenever it hits 88 miles per hour.
If we look at the movie as a whole, the DeLorean is a bit of a MacGuffin: a plot device used to move the movie forward, and in this case, present a problem that the heroes need to resolve. It relies on nuclear fuel to work its time-travel magic which, as Doc Brown sagely notes, isn't "available in every corner drugstore" in 1955. This forces them to find alternative methods to fire up that flux capacitor. (They also revamped this same tactic in the third movie. There, the DeLorean required gasoline to get up to 88 mph, and there was no gasoline in the 1885 setting. Gotta change with the times, you know?)
But none of that answers the question: why use a DeLorean? Why make a time machine out of a car? And why use a car that goofy? The first question was the topic of much debate among the filmmakers, who originally planned to make the time machine out of a refrigerator. But that prompted the concern that little kids would lock themselves in fridges and suffocate, so out that went.
Safety aside, a stationary time machine also presented some logistical problems for the story, since Marty and the Doc would have to run back and forth from its location in order to make the plot work. Throw a set of wheels on it, however, and suddenly all those problems went away. A car was the obvious solution.
Okay, that all checks out so far. But to paraphrase our hero…seriously, a DeLorean? In the name of all things holy, why?
For starters, there's that goofiness factor. It has a distinctive look, with its gull-wing doors and aluminum construction, which makes the whole gag about flying saucers work really well. It was also a bit of a lemon: only about 9,000 DeLorean cars were sold between 1981 and 1983, and they were widely mocked as wonky, under-powered, and basically a great big mistake.
All of that lends the car a very stylized yet slightly scruffy feel, benefiting the plucky underdog vibes that Marty and Doc give out. If the time machine were a Porsche, they'd look a little too confident. If it were a Gremlin, the pathos would be overwhelming. But the DeLorean looked just stylish enough to make an impression while still adding to the sad-sack dilemma of a couple of undermanned nice guys trying to beat the odds. (And as a lemon, it has a way of conking out on them just when the story needs a little complication.)
Oh, and lest we forget, nothing says "1985" more than that car. Pass the scrunchies and leg warmers, Doc: those gull-wing doors look right at home.