The following contains MASSIVE SPOILERS for Avengers: Infinity War. You have nobody to blame but yourself if you keep reading before you see the movie.
Avengers: Infinity War was every bit the paradigm shift of the Marvel Cinematic Universe that we expected it to be, but it was what happened after the credits rolled that really got some people talking. In order to fully get into what happens after the credits, we also need to talk about Avengers: Infinity War ended, so this is your last warning, here there be spoilers.
Unlike recent Marvel movies, who have been piling on the post-credits sequences, with two or more now being commonplace, Avengers: Infinity War harkens back to the original Iron Man from 10 years ago in that the new film only has one scene after the credits, and you have to sit through the entire run of credits to see it. It has one other thing in common with that post-credits scene from Iron Man, Nick Fury.
Infinity War concludes with Thanos having successfully done what he set out to do. He obtains all six Infinity Stones, and with a snap of his fingers, he eliminates half the life in the universe. This includes half of the heroes that fought against him, who vanish into dust one at a time. This is where our post-credits scene begins. We hear it before we see anything, and the voices of two familiar characters is what we hear. One is that of Samuel L. Jackson as Nick Fury, a character who has been MIA throughout the events of Infinity War. The other is actress Colbie Smulders, as Fury's right-hand Maria Hill.
The two are in an SUV traveling down a busy city street. Nick Fury is driving while Hill sits in the passenger seat checking the readout on a machine. She says that a massive energy surge has been detected in Wakanda, something exponentially larger compared to what had been read there previously, during the battle we witness during the main film.
At that moment a car traveling in the opposite direction veers into their lane and Fury has to slam on the breaks to avoid hitting it. After coming to a stop, nothing happens with the car before them. Hill and Fury both exit their own vehicle to investigate but when Hill gets there she finds the passenger compartment empty. A moment later we see a helicopter fall out of the sky and crash into the side of a building. Something has clearly gone terribly wrong here, though neither Fury nor Hill has a clue what it could be.
They both start to head back to their car, but at that moment, Maria Hill begins to feel something happening to her, and she begins to dissolve as we saw so many of our heroes do at the end of the movie proper.
Seeing this, Nick Fury runs back to the SUV. People are panicking in the streets now, some of them dissolving around him. He goes to the back seat of the vehicle where he pulls out an object that is, at first, obscured grom our view. He runs around the back of the SUV, at which point, he himself begins to dissolve. He lets out a perfect Samuel L. Jackson exclamation "Motherf-" before his voice is cut off by his body vanishing into dust.
It's at this point that we finally get a good look at what Nick Fury was holding as it falls to the ground. It's a pager. An old-school, pre-cell phone, pager. It's been modified in some way, but what's more important is that we see that before Nick Fury vanished he was able to successfully send a message on the device. We see the display simply read "sending..." for a few moments before it changes. What we see next isn't a message in text like we might assume, but a simple image. One that looks something like this.
The logo belongs to a character we have yet to meet within the Marvel Cinematic Universe, one Captain Marvel who we will meet when Brie Larson plays the title role in next year's movie of the same name. We can comfortably make the assumption that Nick Fury understands that whatever is happening around is evidence that the Avengers have failed, leading him to make the only other call he can.
The scene makes perfect sense based on what we know of the Captain Marvel movie so far. It will be set in the 1990s, pre-dating Iron Man and most of the rest of the MCU. We know that Nick Fury will also play a key role in the movie. It appears that Fury has kept this pager with him on a regular basis just in case he was to need it, as he does now. It's likely a direct line to Captain Marvel. It's a humorously fitting way to communicate, as nothing quite says "early 90s" like a pager.
This implies that while Marvel may have wanted Fury to have a way to contact her, the two have not been in contact in decades as, if they had met more recently, she probably would have replaced the pager with a burner phone.
The fact that the pager appears to have been modified is also interesting. This could be for any number of reasons. Perhaps a special battery has been added to ensure the AA Duracell's didn't need to be replaced every few weeks. Perhaps, this pager sends a different sort of signal, one that Captain Marvel can notice directly so that she doesn't need to carry a pager around with her. Maybe it allows the pager to send a signal to outer space. We know that the Captain Marvel movie will see her fight the alien Kree, and if she hasn't been on Earth for the last couple decades, it would explain why she hasn't shown up during any of the previous world-ending catastrophes within the Marvel Cinematic Universe.
Odds are we'll see this pager again at the end of Captain Marvel When Nick Fury receives it. Then we'll see her give the Avengers whatever aid she can when Avengers 4 comes around next year.