We have no idea what a Grand Moff is, but we assume it is the highest honorary title the Villain Order of Discontent may bestow on its members. Because Grand Moff Tarkin is one bad guy.
Tarkin is not the supreme leader of the Empire—that dishonor goes to the Emperor—but he is the commander of the Imperial military. He is so high up the chain of command that he can order Darth Vader around. He tells Vader to release that Imperial Officer from the Force choke and Vader obeys right away.
Tarkin's main goal is to expand fear of the Empire throughout the galaxy. As he puts it: "Fear will keep the local systems in line—fear of this battle station." By making leaders and their constituents afraid of the Empire, Tarkin ensures they will step in line with the Empire's demands.
This is why he chooses Alderaan for the test run of the Death Star's laser. He doesn't want a planet that is "too remote to make an effective demonstration"; he wants the galaxy to see what he and the Death Star are capable of.
This does lead to one problem for him: the Rebellion. It's kind of difficult to sow the seeds of fear when a small group of ragtag warriors keep not doing what you tell them to. Not that he thinks they are a true threat; he thinks they're more of a nuisance.
As he puts it, the Death Star will allow them to "crush the rebellion with one swift stroke" (Star Wars). Even during the Death Star assault, when the rebel's attack is shown to be exploiting a potential weakness, Tarkin's pride doesn't allow him to take the safety precaution and evacuate. "Evacuate in our moment of triumph?" he scoffs. "I think you overestimate their chances."
Tarkin pays the ultimate price for his pride though and is killed when Luke destroys the Death Star.