What's the meaning of “411 on the late-night drop box”?

Question

Nick Fury walks up behind Captain Marvel:

Nick Fury: Uh, I'd like to ask you some questions. Maybe give you the 411 on the late-night drop box. Could I see some identification, please?

What's the meaning of "411 on the late-night drop box"?

Answer 1

"The 411" is a reference to requesting (or in this case giving) information. It's listed in Maciej Widawski's African American Slang as

"Information or fact"

A "late night drop box" was used by Blockbuster Videos to allow customers to drop off their videos when the store was closed.

Fury is referencing the fact that she likely just blew a hole in the roof of the nearby blockbuster rather than (haha) using the drop box to drop off her video. He's going to explain to her how the system is supposed to work.

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In-universe it's likely he was amusing himself but also opening with a line that's intended to determine whether she a) knows anything about the explosion and b) is trying to determine if she's the agent of a foreign power who may not know American colloquialisms.

Out-of-universe, using slang is a way of continually reinforcing with the audience that this is a young(er) hip(per) version of Fury. This would also tie in with Fury's fictional upbringing in New York.

Answer 2

411 is a special telephone number for information.

Blockbuster was the dominant video rental store. In the 80s, videos were too expensive to own, so you rented.

You had to bring the videotape back when you were done (Be kind! please rewind!) Blockbuster had long hours, but if you returned so late-night that the store was closed, there was a drop box

give you the 411 on the late-night drop box

give you the correct information on the normal way to return Blockbuster videos after-hours... (Because, apparently, you don't know).

Giving a person unneeded information (how to use the drop box) is a style of condescension, as you see in Office Space with the TPS reports. This is playful/sarcastic/snarky (especially in this case, since it contradicts itself by implying Danvers was smart enough to parse the cultural references).

It was Fury's way of conveying authority without being excessively overbearing/authoritative.