When it comes to the original Star Wars trilogy, there's really only one villain that people remember: Darth Vader. However, the first film had another character that was just as cruel, if not more so, and since Rogue One: A Star Wars Story is taking us back to that era, it's important that we remember him. While much of Wilhuf Tarkin's history has been rewritten since Disney picked up Lucasfilm, the character has actually been a significant focus in the recent ancillary material, so we know quite a bit about who he is.
We first meet Wilhulf Tarkin, chronologically, as a Captain in the Republic Navy in The Clone Wars TV series. While he's on the same side as the rest of our heroes, he's clearly somewhat hostile to our Jedi friends. He finds himself at odds with Anakin Skywalker at one point on the field of battle and he heads the prosecution of Anakin's padawan Ahsoka when he believes she is guilty of murder. By then, he has obtained the rank of Admiral. It's also revealed here that Tarkin is already a friend of Chancellor Palpatine, though it's not clear that he knows any more about him than Anakin Skywalker does at this point.
We then fast forward a few years and join the novel Star Wars: Tarkin, which shows us the first time that the Admiral meets Darth Vader. Tarkin and Vader work together at the behest of the Emperor to hunt down some dissidents who attacked a base that Tarkin had been in charge of. It's during this mission that Tarkin and Vader gain a mutual respect for each other which leads to them working so closely together in the original Star Wars. After successfully completing the mission, the Emperor bestows the title of Grand Moff on Tarkin, the first person to ever receive it.
From here, it becomes clear that Tarkin is one of the Emperor's chief lieutenants. He's named Governor of the Outer Rim by the Emperor and responds personally to rumors that there may be a Jedi inciting rebels on an Outer Rim planet in the animated series Rebels. However, most of his activities are focused on the construction of the Death Star. In the final scene of Star Wars Episode III: Revenge of the Sith, we see Darth Vader and Grand Moff Tarkin standing on the bridge of a Star Destroyer viewing the construction of the Death Star. It's clear that Tarkin's connection to the station was strong from very early.
The Star Wars novel Catalyst shows us that that Tarkin and Advanced Weapons Director Orson Krennic did not work well together during the battle station's construction. Krennic actually takes steps to make Tarkin's job more difficult in order to make himself look better in the eyes of the Emperor. Tarkin, for his part, employs a spy to report on Krennic's activities. When the novel ends, Tarkin is responsible for security of the Death Star project, but he has his eye on taking over the entire thing.
When Star Wars opens Grand Moff Tarkin is in control of the Death Star, so we know that his plan was ultimately successful. How much of this we'll see in Rogue One: A Star Wars Story is unclear, though everything we've heard seems to confirm that Grand Moff Tarkin will be an important character in the film. We've even seen him in the trailer.
Exactly how big a role Grand Moff Tarkin will play in Rogue One: A Star Wars Story is not clear, but based on the fact that Ben Mendelsohn's Director Krennic is the lead villain of the piece, it would seem that he's still in charge of the Death Star program at this point. We will probably see what steps Tarkin takes to undermine his rival and take the project away. With Peter Cushing obviously gone, any attempt to put Tarkin into Rogue One will need to be done through some digital effects that will need to be impressive in order to do the job right.
Once he does successfully take over the Death Star, Grand Moff Tarkin is actually the primary antagonist of Star Wars. Princess Leia describes him as holding Vader's leash, implying that Vader is only the muscle of the operation, Tarkin is the one truly in charge, a situation which, as far as we know at this point, Vader is ok with. Rogue One may give us more insight into this relationship as well.
Of course, getting what he wanted eventually led to Wilhuf Tarkin's destruction. Because he was on board the Death Star during the rebel attack, he was there when it was destroyed. He refused to be evacuated and it's hard to believe there's any way he could have survived. Though, to be fair, some have argued exactly that.
While his time in the film series is limited compared to most, Grand Moff Tarkin is still an important character. Now that you know everything about him, you're ready to learn the rest of his story in Rogue One.