Shazam! spoilers ahead. A post- or mid-credits scene in a superhero movie is a nod to the fact that, in comic books, these stories go on and on and on. They're also a nod to the fact that a sequel is (probably) coming. The mid- and post-credits scenes in Shazam! are no different: The mid-credits scene shows what the movie's big villain is up to after the final battle, and the post-credit scene just leaves viewers with another little joke.
At the end of the film, Shazam/Billy Batson (Zachary Levi/Asher Angel) and the Shazam Family successfully defeat Dr. Thaddeus Sivana (Mark Strong) and the demons representing the seven deadly sins that have been controlling him. We see that Billy and the rest of his foster siblings (who can now all become superheroes by saying "shazam") continue on with their lives and even meet Superman, but we don't see exactly what happens to Dr. Sivana until the mid-credits scene.
In this short scene, Sivana is shown in what appears to be a solitary confinement prison cell. As one always does in solitary confinement in a movie, he's scratching drawings all over the walls. The drawings are of the symbols that one sees before they are sent to the wizard Shazam's (Djimon Hounsou) lair. When Sivana previously figured out the order of the symbols earlier in the movie, he was able to go back to the lair where he was summoned as a child, but that time, he turned fully evil and was taken over by the demons.
While he's drawing on the walls, suddenly there's a voice that says, "You assume there's only one way..." It's then revealed that the voice is coming from a caterpillar-like creature that's standing on a ledge in the room. Hmm... Looks like Sivana's going to find another way out after all.
If you don't know anything about the actual Shazam comics, then this whole thing is probably quite a surprise. But, this caterpillar guy has a name and a long history.
The creature is named Mister Mind and, according to the DC Fandom site, he is a diabolical worm from Venus with unmatched mind control powers. He is also the leader of the Monster Society of Evil, and, yes, he does team up with Sivana. The original version of Mister Mind first appeared in 1943 in Captain Marvel Adventures #26. (The hero Shazam used to be called Captain Marvel, but due to ownership and legal issues over the years that has obviously changed.)
Bounding Into Comics points out that some viewers may have spotted Mister Mind earlier in the movie. According to the site, "The mid-credit scene shouldn’t actually surprise keen-eyed viewers who spotted a certain Captain Marvel villain being housed in the Rock of Eternity. However, after Sivana’s attack where he releases the Seven Deadly Sins, the little green guy is nowhere to be seen. In fact, his glass cage is broken."
As for the post-credits scene at the very end, it doesn't give any real new information or set up a sequel, but it does connect the movie to another DC hero. Earlier in Shazam!, Billy's foster brother, Freddy, helps him test his powers to find out which ones he actually holds. In the bonus scene at the end, they're shown testing whether Billy can communicate with fish like Aquaman by having him focus on a goldfish in a bowl. As Games Radar explains, "It’s a goofy little palate cleanser at the end of an extremely enjoyable film, and it’s nice to see that Aquaman doesn’t get left out after Wonder Woman, Batman, and Superman are all referenced at various points throughout."
It's unclear what the future holds for Shazam on film right now, but per these scenes, the hero could end up battling Mister Mind or teaming up with someone who actually can talk to fish. With his powers, the possibilities are endless.