Interdimensional drives are often confused with hyperdrives, and many science fiction sources freely mix and match their features. They do use similar principles--shunting the ship into a universe other than the one we’re familiar with to bypass huge distances--but in truth are distinctly different. (Note: The TV series Earth: Final Conflict employed a means of FTL travel called an interdimensional drive, but that worked very differently from what’s described here.)
STANDARD INTERDIMENSIONAL DRIVE
Tech Level: 19
Interdimensional drives work on the principle that our universe is not unique. That there is, in fact, an infinite number of universes that exist alongside our own, created simultaneously with our own Big Bang, a mere quantum vibration or Planck-scale right turn away. Anyone familiar with the concept of alternate realities or divergent histories or with Everett’s "Many Worlds" interpretation of quantum physics is probably already conversant with the idea. The TV series Sliders and the "mirror universe" episodes of different Star Trek series are probably the best known examples of this concept in science fiction.
How exactly one could access these "parallel" realities, if they exist, is a matter of some debate. As with many other FTL schemes, the means required would depend much more on the nature of the universe (or multiverse, in this case) turning out a certain way than on just raw technical sophistication. Most "other" dimensions are considered to be separated from ours by some group of quantum properties unique them, such as different "vibrational" Planck-scale wavelengths or electron spin resonance or some such. Therefore, accessing these other realities would depend on the warping of space by gravity manipulation or the use of advanced quantum-force manipulation or a combination thereof. The most common motif, popularized by Sliders and other recent SF sources, is the use of a wormhole to open an actual doorway into other dimensions.
However, the topologies of the many various realities are not necessarily in synch. Three-dimensional coordinates in one universe does not necessarily correspond with those of one right next door. In other words, if you were on Earth when you shifted realities, you would not necessarily end up on the same spot on the Earth in the new universe--you may end up in the middle of the ocean, in orbit, on Mars, or even halfway across the cosmos. It would all depend on how the four-dimensional curvature of the originating universe lined up with that of the target universe.
So, basically, by using interdimensional travel, one could theoretically enter another universe, take three steps to the right, re-enter our universe, and end up galaxies away.
Of course, not all alternate cosmos would necessarily have the properties to be conducive to this sort of travel, and those that are would need to be mapped for entrance and exit junction points that offer the fastest and best travel. Worse yet, the coordinates may not remain in static correspondence--their relationship may shift over time, so that a route that led to another galaxy one time may lead only to the closet down the hall the next.
Also, there is the problem that temporally the universes may not line up in synch either, meaning that transitioning briefly to another universe may shift you moments, or centuries, or eons into your past or future as you re-enter your home reality.
These drives provide the ship with no particular protection against interdimensional physical property changes; the ship is completely subject to the physical laws of the newly-entered universe, whether they be friendly or hostile to the ship’s well being. Usually, when employing these "naked" ID drives, a ship must by necessity only enter universes with physical laws are close if not identical to its own, or risk all kind of unpleasant consequences.
SHIELDED INTERDIMENSIONAL DRIVE
Tech Level: 21
Another hazard with using interdimensional travel as an FTL option is that not all universes will end up having the same physical laws. When a ship enters a new reality, it becomes a part of that reality and is subject to its physical laws. This is good in some ways, as one universe’s properties may result in the compression of space or greatly expanded values of lightspeed or some such, meaning that even in a straight coordinate-to-coordinate match between two universes a ship can still use the "new" universe to cheat the lightspeed limitations in its "old" universe.
However, even a small change in many physical laws would result in delicate and complex biological systems--like the human body--to go haywire or stop functioning altogether. Our lives literally depend on many universal values to remain exactly he same from one moment to the next. Slightly lower physical constants of friction, for example, would have the heart pump blood at hundreds of miles an hour into the bloodstream; shifts in the value of the amount of charge an electron can carry would result in our nervous system frying itself; a decrease in how strong the Van Der Walls forces, the forces that hold molecules together, could result in crewmen being vibrated into puddles of monomolecular goo just by the force of inhaling a breath. And so on and so forth.
In order to avoid this hazard, one solution is for the ship to "carry" a bubble of its own universe with it, to act as a buffer or shield against the ravages of the physical oddities of its transitional reality. Just before it enters a new universe, the ship "folds" a bubble of its originating universe around itself, where its old physical laws still apply. This is in fact very similar to the warp bubbles used in Warp Drives, but instead of facilitating travel the bubble is used to preserve the ship against hostile physical universes.
Just how stable this bubble of "normalcy" would be is unknown. It might be very stoic, lasting without a scratch for as long as needed, or it might slowly wear away or degrade the longer the ship is in the hostile universe, dictating the length of FTL sojourns by how long the bubble can last. Having the bubble seriously degrade would be a terrifying experience for those aboard an Interdimensional Drive ship, because it wouldn’t just "pop" or physically wear down such like a normal bubble. Rather, the physical laws of the new universe would simply, inexorably, begin asserting themselves and the bodies of the crew and their ship around them would slowly begin to break down...
The "hyperdrive" of the Traveller RPG universe acts very similarly to an Interdimensional Drive, including the use of a "normalcy bubbles" (called "jump bubbles" in the game) to protect hyperdrive ships from the hostile physical laws of its hyperspaces.
Sliders, et al
Star Trek, et al
Traveller RPG, et al.