Tech-Priests Dominus (also known as Magi Dominus) are high ranking members of the Adeptus Mechanicus, usually playing a very important role in many orders of the Cult Mechanicus. Usually senior Magos with centuries of experience, they are designated to command the military forces of the Adeptus Mechanicus, usually leading the Skitarii Legions, the electric smurfs, the Knight Houses and the Legio Cybernetica to battle, while also continuing the Quest for Knowledge. Despite being incredibly wise and knowledgeable individuals, the Tech Priest Dominus are usually only used as generals in battle, in particular to make sure the associated forces of the Mechanicum work alongside the Skitarii without problem.
In the Fluff
During the early days of the Imperium, the Magos Dominus were the ones in charge to continue the investigation and exploration for more DAoT stuff, as well as for their maintenance. In particular, they were in charge of the Legio Cybernetica (though now in 40k they aren't limited to it), and while this gave them a lot of prestige and influence, the ancient robots were still seen with suspicion and caution, so were used as the scapegoat to heavily control the Magos Dominus' chances to climb the ranks. This means that the amount of byzantine in-fighting in the Mechanicum guarantees that some of the most knowledgeable people in all of the Imperium are sent to the frontline by the schemes and machinations of their fellow Mechanicum, to be moved out of the way. This has forced the Tech Priest Dominus to be incredibly adept at war, thanks to both their ability to analyze and process every single element on the battlefield to turn them against their enemies and to their incredible resilience, born from hundreds and hundreds of augmentations. Augmentations that wildly vary from Magos to Magos depending on their specialization. To give you an idea of how actually badass these aspergers can be there is one narration in Horus Heresy Book One: Betrayal (pg.58) where one Calleb Decima brings down 2 Fellblades, annihilating the first one with a sort of modified teleporting device and jumping into the second in the middle of a firefight and hijacking it, read, killing the traitor marines crew all by himself and taking control of the tank systems, Rules of Nature may or may not have been playing in the background while he was doing all of this.
The most famous of Tech Priest Dominus in current 40k is "Archmagos Dominus" Belisarius Cawl, and he's also the most powerful of the whole Mechanicum thanks to his ties to Bobby G, only limited by the fact he's not the Fabricator-General of Mars, though he's probably working on that now, did we mention he scammed a C'tan shard while in the middle of a collapsing Necron tomb complex?
On the Tabletop
The Tech-Priests Dominus are the basic HQ of choice if you don't want to go for Martian FORGE WORLD (If you do, you pick Cawl). For 80 points, you get a strong unit that repairs and boosts your vehicles while not being too bad at fighting itself. If you want more info, you can go to the 8th Edition tactics page.