Well, first: Why is the movie called Midnight Special? The closing credits feature the traditional folk song , but—trust me—that doesn't answer the question.
It's questions like this that makes me happy to be a skilled Google querier. Here's the answer, such as it is, from writer/director Jeff Nichols:
Q: Let's start with the title, Midnight Special. Why did you decide to call it that?
A: Well to be honest, you know, when I was still developing the story I was just mainly thinking about the genre elements. I hadn't really attached all the personal elements from my life yet, and when I was thinking about it kind of simply as a genre film, it's kind of this badass homage '70's and '80's sci-fi chase movies. I just thought of – I thought of that title and I thought it sounded tough, I thought it sounded cool and I thought it was evocative of the style of film. I wanted it to make it sound like a midnight drive-in movie or something, it just felt kind of muscular, just felt cool. I was a big fan of the song, but there was no real direct connection at that time to the plot, although maybe they kind of crept into my mind through osmosis or something...it's a great song, and I thought it was a cool title.
So… now we know. Sort of. We also know that Jeff is not the kind of guy to just say "I thought it was a cool title" right up front.
The movie, to its credit, starts off on the run: guys named Roy (Michael Shannon) and Lucas (Joel Edgerton) are on the lam with a kid named Alton (Jaeden Lieberher, the hero from It). The cops are in pursuit, an Amber Alert has been issued, …
The movie gradually fills in the answers to all the what's-going-on questions. All is not as it seems. Alton has Strange Powers. Roy is his bio-dad, and whatever their other flaws, he and Lucas have his best interests at heart. And it turns out they're not only on the run from the normal cops, but also a wacky religious cult (led by Sam Shepard in one of his last movies) and the full force of the FBI/CIA/NSA/DHS/etc.
There are a lot of did-not-see-that-coming plot elements. I like those a lot.
All the acting is first-rate. Especially good is Adam Driver in a pre-Kylo Ren role as a sympathetically nerdy NSA analyst. (And I couldn't help but think how much better he is in this role than he is as Kylo Ren.)