Artificial gravity

Artificial gravity is a technology employed by the UNSC, Covenant and Forerunner technology, to generate gravity of varying strengths.

Centrifugal Motion
Prior to contact with the advanced technology of the Covenant, a number of UNSC ships employed rotating sections of the hull to provide centrifugal and centripetal forces on the interior of the hull to allow comfortable movement in "gravity." Carriers were able to adjust the rate of rotation, allowing more or less gravity, and a number of other ship classes, such as Halcyon-class Cruiser's, also used rotating sections before the introduction of reverse engineered gravity plating.

The Halo Installations apparently rotate, and may use centrifugal force to provide at least part of their Earth-like gravity, possibly employing the same gravity generation techniques used by the Covenant, or another method, to generate the rest.

Covenant Artificial Gravity
In contrast, almost all Covenant vessels employ some sort of artificial gravity mechanism that does not involve rotating hull sections. Instead, their method allows for the generation of actual gravity, or alternatively diamagnetism, through artificial means, or by using ultra-dense materials which generate their own gravity, a means not beyond their level of sophistication.

Although the UNSC experimented with true artificial gravity prior to First Contact, most attempts were unsuccessful, or produced mixed results. They generated an artificial gravity field, but were too dangerous and unpredictable to use in ships, with some passing into rebel possession. After contact with the Covenant, however, reverse-engineering Covenant technology allowed the UNSC to employ artificial gravity on most of its ships.

If the method used by the UNSC and the Covenant is indeed diamagnetism, using the body's own magnetic field to draw it towards the generator, then the health effects would be unclear, but likely detrimental. However, the use of dense materials with their own gravity would have relatively few side-effects, being actual gravity, but dramatically increase the mass of the ship, hindering propulsion. If the UNSC did acquire artificial gravity technology from the covenant, then this technology was definitely not based around ultra-dense materials, as human propulsion systems clearly cannot deliver enough thrust to move such a massive object.

Discrepancies
It is widely agreed that the UNSC gained their current artificial gravity technology from the Covenant, and had to use rotating centrifuges to mimic gravity prior to this. However, the Halcyon-class cruisers and Phoenix-class colony ships clearly lack rotating centrifuges (although the former is described to the contrary in the novels), and both were originally commissioned far before first contact with the Covenant. Of course, it is possible that both classes were designed to lack gravity altogether, and were retrofitted with artificial gravity later in their service lives. However, if this is not the case, then it appears that the UNSC did in fact possess true artificial gravity technology before the Human-Covenant War.

The situation is further complicated by the human DCS freighters. Descriptions in Halo: Contact Harvest (set at the time of Covenant first contact) clearly suggest that some form of gravity was in play aboard the vessels, but the novel fails to mention its nature. It may be that antigravity plates (as seen in Halo: Ghosts of Onyx, said to have not "panned out") were undergoing trial runs aboard all of the vessels formerly mentioned, but this seems slightly far-fetched.

Trivia

 * Eugene Podkletnov has claimed that he has designed a device that can create artificial gravity. In contrast, a group funded by the ESA, claim to have developed a device that reduces the effect of gravity. The validity of these claims are unclear.
 * Artificial Gravity is a popular concept among science fiction novels, television shows and films, but attempts to explain their workings are usually implausible, involving gravity field generators.