Enginseers (Not to be confused with the Eldar Farseer or Spiritseer) are members of the Mechanicus. They differ from Tech Priests in that Enginseers are more combat orientated and are the only few members from the Machine Cult that work for the other organizations of the Imperium (Enginseers are, quite hilariously, part of the Tithe the Adeptus Mechanicus gives the Imperium every so often along with the spaceships/tanks/guns/ammo/etc... They're a kind of glorified indentured servant.) Prominently, they accompany the Imperial Guard where they basically have the role of mechanics and maintenance crews, making sure the humongous amount of flashlights, tanks and other tools of war are always up and running.
You know those Tech Priests from the original Dawn of War games? Yeah, technically they should be Enginseers, but Relic and THQ probably stuck with Tech Priests as they are probably easier to remember and won't get confused with the Farseers. (Giving Relic a lot of faith there. They probably just didn't do their research)
Enginseers first and foremost are highly trained members of the Cult Mechanicus and are dedicated to the maintenance of Imperial technology. While Tech Priests may venture out and explore undiscovered locations for more goodies to hoard, Enginseers stay back to help other Imperial Organizations in order to keep their stuff running and maintain a stable relationship with the wider Imperium. They are a common sight on battlefields with large numbers of armoured vehicles, and are often accompanied by a retinue of servitors for assistance or protection. Although most Guardsmen revere their vehicles enough not to risk annoying an Enginseer by 'tinkering,' the modification of vehicles to fulfill a certain need is inevitable, much to the chagrin of any Enginseers present. Enginseer contingents are also included in the mighty Titan Legions and the crews of the massive warships of the Imperial Navy, allowing them to perform emergency repairs in the heat of battle.
Humorously, despite the respect they usually command among the units they are seconded to, Enginseers are not held in high regard among the Cult Mechanicus itself as their skills seldom contribute to The Quest for Knowledge. As a result of their overwhelmingly practical knowledge, they are often viewed as lowly but necessary cogs in the workings of the Cult.
Enginseers make use of robotic arm augmentations known as Mechadendrites that are connected to their central nervous system via the spine. They are used to help the enginseer in repair operations, heavy lifting and for self defense.
In 8th edition Enginseers are vital to the AdMech player. They are the only cheap HQ so you want to spam probably 2-3 of them. Problem is that they cost 30$ each. There's a simple solution to that. Some of the robed model in the cultists kit included with Dark Vengeance look remarkably adeptus mechanicus like. One of them even has an axe that look remarkably like an omnissian axe. You can buy a whole squad for a couple of bucks from ebay. Pick one of them, glue some bits that you have left around from skitarii, tech priests, onagers whatever and you have a nice 2$ enginseer. With a disturbing chaotic look.