The DeLorean was famous but it wasn't popular in the sense that a lot of people bought one.

It was famous because the guy who owned the DeLorean Motor Company, named John DeLorean, had been arrested by the FBI for smuggling millions of dollars worth of cocaine into the U.S. He was arrested with a suitcase full of cocaine and the allegation was that he intended to use the money from selling the cocaine to help his failing car company, which was not selling many DeLoreans.

But he was never convicted because he argued that he was entrapped by the FBI, and the jury found him not guilty.

The story was all over the news. A lot of people viewed the situation as humorous more than as some great criminal enterprise because attitudes towards cocaine in the U.S. weren't as negative at that time as they are now (this changed later when crack cocaine came along).

This all happened a few years before Back to the Future was released. So when the movie was released, the whole DeLorean story made the use of the car in the movie kind of inherently funny, like "hahaha they're using a DeLorean!!"

You can get that sense from the movie's dialogue, where Marty can't believe it but out-of-touch Doc Brown thinks it's a cool car:

"Marty McFly: Wait a minute, Doc. Ah... Are you telling me that you built a time machine... out of a DeLorean?

Dr. Emmett Brown: The way I see it, if you're gonna build a time machine into a car, why not do it with some style? Besides, the stainless steel construction made the flux disperal... Watch out!"