In many sci fi games we see vehicles (or in halo 4 and 5 guns) that use hover technology. But how using technology that is scientifically realistic could we explain military grade hover technology? By hover I mean that when it is turned on the vehicle will hover off of the ground by around 1-2 feet.
Use Arthur C. Clarke's rule, "Any sufficiently advanced technology is indistinguishable from magic," followed by Sanderson's First Law of Magic, "An author's ability to resolve conflict with magic is DIRECTLY PROPORTIONAL to the readers' understand of said magic."
The problem with most hover technologies that actually exist is that they tend to work very well in carefully structured environments, but the math simply forbids them from working in open air. You can levitate a frog in a magnet using its diamagnetic properties, but that required a tremendously powerful magnet that weighs many times more than the frog and would have to be levitated along with it, creating a chicken and the egg problem. Antigravity theores have been theorized, but since we are yet to observe a gravaton, we're not really sure how they work. Other approaches work great when you're in a constrained environment (such as a magnetic monorail), but don't work so well once you're far off the ground.
You will have more success hand waving it away as technology that doesn't need to be understood. Use Sanderson's law, and write the story such that the reader really doesn't need to know much about the hover technology. One easy way to do that is to have the characters not really understand how it works, and have to "trust the system" every time they get into their vehicle. Don't feel obliged to explain everything about your world — leave some mystery in it!
One technological detail you should get right, even if you handwave it, is the energy required. I can "levitate" an object by putting a physical support underneath it, and it takes no energy, so if your levitation system just hovers without moving up or down, it doesn't have any specific energy requirements. However, if you can hover up or down, it must be in a position to deal with the potential energy shift that occurs as you move up. If the hover technology can move you upwards, it probably shouldn't be powered on AA batteries.
Or, if you are dead set on an explained source of military hover technology, use hover technologies which are already battle proven:
By hover technology I presume you actually mean anti gravity.
Since gravity is usually described as the warping of space-time under the influence of a massive body (like a planet or a star), what is actually being asked for is to create a "spike" that rises out of the gravity well that the object balances upon. This would involve warping space-time in the opposite direction, and in a very narrow and focused area. If you were to use the standard image of a bowling ball warping a flat rubber sheet into a bowl shape, then the "anti gravity" region would be using a chopstick to poke the rubber sheet from the bottom and push back up level with the flat region.
This would involve a lot of energy (overcoming the local gravitational warping of space-time), as well as some near lightspeed handwaving, since there is no known technology that could do this. I suppose if you wanted to use brute force, you could arrange to have a similarly sized planet directly overhead, cancelling out the gravitational influence of the planet you are standing on in that region (you can extend that analogy by substituting a smaller slug of neutronium or even a micro black hole hovering overhead, but there would be some obvious difficulties with any of these solutions).
For the purposes of the story, you could obliquely refer to warping the gravity well and the energies required to do so, without going into much actual detail (a novel about air combat could mention the static and afterburning thrust of the engine of an F-35, without going into any detail about how the engine was arranged or worked). Have fun!
Whilst most of the answers given seem to focus on hover tech blocking gravity, or "sitting" on magnetic fields, there is a possibly more likely version:
Assume, for the sake of the argument, that some manner of energy-based propulsion tech exists (the big glowing plasma drive-type thing). The extension of this would be to miniaturise it and place a control circuit in to simply counteract gravity, no different from the jets which are able to do vertical take-off and landing.
If such a tech exists, and is cheaper/easier than conventional combustion jets, it would not be beyond reason that such a system, and the moderate energy required to propel in a specific direction, would be more beneficial for ground vehicles (particularly when dealing with hostile terrain).
If you want to make a defined difference between the ground-based vehicles, and the flying ones, then the additional control systems required to deal with full-flight would be more expensive to produce, and more difficult to control.
If you introduce the (techno-magical) ability to create narrow beams of electric or magnetic forces, then a GPS-like system of force-beam satellites could do it. There's no known phenomenon that could create these beams, but if we could, everything else is bog-standard physics.
Remember to include ground stations to beam a counter-force back to the satellites, since they'd be attracted to the ground with the same force they're applying to hover-vehicles.
If you simply need a military hovercraft that can operate realistically, why not use the real ones?
Hovercraft use blowers to produce a large volume of air below the hull that is slightly above atmospheric pressure. The pressure difference between the higher pressure air below the hull and lower pressure ambient air above it produces lift, which causes the hull to float above the running surface. For stability reasons, the air is typically blown through slots or holes around the outside of a disk- or oval-shaped platform, giving most hovercraft a characteristic rounded-rectangle shape. Typically this cushion is contained within a flexible "skirt", which allows the vehicle to travel over small obstructions without damage.
This is not anti-gravity or magnetic, but it is wheelless and does not touch the ground.
Why not make these into flying cars? Mostly because they are horrid in fuel mileage compared to something with wheels or even wings. They are only competitive with helicopters.
The primary use of hovercraft in the real world is for use over surfaces into which ground vehicles would sink but which don't have a consistent enough depth for water vehicles. They can handle water and land as well as shallows and swamps. This flexibility gives them an advantage over boats and cars. Unlike winged vehicles, they can pause and stay in one place.
They are cheaper to operate than helicopters, and they have a higher weight capacity for the space they take than helicopters. The latter reason is why marines use them for water to land attacks. The former reason is why emergency crews use them--in floods for example.
Why might your characters use them? If energy is cheap enough in your world, perhaps the fuel mileage costs don't matter. If energy is cheap enough, you can even do without the skirts. There are hovercraft that can go as high as fifty feet. The skirts do make it easier for people to walk close to the hovercraft, as they reduce the airflow needed to stay off the ground.