Spoilers ahead. In the new Aquaman movie, out Dec. 21, there are two villains: Aquaman's half-brother Orm (Patrick Wilson), who wants to be defeat Aquaman (Jason Momoa) and become Ocean Master (really, Ocean Master) and Black Manta (Yahya Abdul-Mateen II), who starts working for Orm and wants Aquaman dead because Aquaman kinda, sorta killed his father. Both of these characters exist in the comics, but given his trajectory in the movie, you might want to know more about Black Manta in the Aquaman DC comics. After all, if this thing has a sequel, he'll almost certainly be back.
The first big fight scene in the movie is between Arthur Curry/Aquaman and some heavily armored American pirates up to no good on a Russian submarine. The confrontation ends with Aquaman leaving one of the pirates to drown in the flooding submarine with his son, David, the only one left who can save him. But — twist! — David does not save his father, because his father kills himself more quickly than he would have drowned. The reasoning here being that the dad knows his son would be risking his own life trying to save him and he wants him all fired up to go seek revenge on Aquaman. (It's not great reasoning, but hey, these are evil people we're dealing with.)
David survives, teams up with Orm to kill Aquaman, gets some even more intense Atlantean armor, and becomes Black Manta, named after his grandfather who was known in the Navy as Manta. Yadda, yadda, yadda, he doesn't defeat Aquaman, but he does return in the mid-credits scene and is saved by Dr. Stephen Shin (Randall Park), a conspiracy theorist who is obsessed with finding out more about Atlantis.
So, that's the basics of what happens with Manta in the movie. As for the comics, Manta's story is kind of all over the place, but he's been an Aquaman villain for a very long time. Manta first appeared in 1967 in the comic Aquaman #35. (Aquaman himself debuted in More Fun Comics #73 in 1941.)
As explained by IGN, Manta has gone through a few reinventions over the years when it comes to why he and Aquaman are at odds. When he was first introduced, it was unclear why he held such a grudge against the superhero, and it took 10 years until readers got to see what he looks like under his helmet. As in the movie, he is a black man in the comics and, according to IGN, was interested in Atlantis as a place where "his people" could find a new life. It was also in a 1977 comic that Manta killed Aquaman's infant son, Aquababy, according to Den of Geek, by, essentially, drowning him.
Both IGN and Deek of Geek note that Black Manta didn't get a true origin story until 1992 in Aquaman Vol. 4 #6, where it was explained that as a child, Manta was kidnapped and forced to work on a ship. He turned against Aquaman after Manta tried to get the hero to save him and he didn't. There was then another origin story in 2003 in which Manta was put in an asylum as a child, which messed with his mind, but also gave him powers.
Then, in the New 52 comics (these were 52 new #1 issues that DC put out in 2011), Manta and Aquaman had a run-in that is more similar to the one in the movie. As explained by Black Girl Nerds, in the New 52, Aquaman kills Black Manta's dad as revenge for him causing his own dad's death. So, not quite what we see in the new film, but Aquaman is responsible (with varying degrees of directness) for Manta's father's death in both that comic and in the movie.
Since Manta pops up in the mid-credits scene, there's a good chance he'll be back if an Aquaman sequel happens.