The Force is a supernatural energy field derived from all living things in the Star Wars galaxy which binds them together. A few individuals are sensitive to The Force and can make use of it, though they are also influenced by it.
Certain individuals are born with an affinity towards The Force and as such can use it a wide variety of ways. Likewise it exerts itself onto them as they use it.
What is the Force?
In the Original Trilogy, the Force was accepted to be a mystical, quasi-religious power that exists in and permeates all life forms to greater or lesser degrees, not unlike qi in Chinese mythology and martial arts. During Episode 1, however, George Lucas decided that he needed a more tangible explanation for the Force to explain why Anakin Skywalker was so much better than any Jedi, so he came up with the explanation that the ability to actually connect to the Force stems from the presence of symbiotic micro-organisms called "Midichlorians"; the more of these an individual has, the stronger their connection to the Force and the better their ability to use its energies. Despite what a lot of people will tell you, they don't create the Force, they just govern your ability to access it. Think of them as biochemical sockets tapping into the Force. Force Users have a higher than average count of these midichlorians, and how much higher than average this count is determines how powerful a Force User can actually be. One of the appeals of the Dark Side, then, is the ability to circumvent this built-in "power limit", kind of like switching from AC current to DC current, although channeling more power than your physical limits can handle will do a number on you, which is only expected when you're talking about forcing the equivalent of high voltage through your brain.
Because this explanation was considered very skub, it was never brought up again and quietly reverted back to its mystical roots.
The Light and Dark Sides
A key aspect of The Force is the dichotomy between the Light Side and the Dark Side. The Light Side is linked with self control, altruism, a love for all life and a desire for harmony both internal and external. The Dark Side is linked with selfishness, passions left to run wild and a desire for power. The most well known users of the Light Side of the Force are the Jedi and the most well known users of the Dark Side are the Sith, though neither of which are the exclusive users of either one.
The Light is also entirely passive; it is a choice not to act but to observe, judge, endure, and heal. The Dark is active; it attacks, conquers, and desires. The Light is waning in strength for those who are lost or loose control. Anger, desire, and hatred from The Dark simply flow more freely and give more ready power to those who haven't devoted themselves to acetic nonaction. With a complete and holistic study and devotion, however, The Light has a greater ability to guide and strengthen.
The Force is constantly in turmoil with itself between Light and Darkness, forever pushing towards an balance which it can never fully achieve. It is also notable that individuals who use the force can get caught up in the pull of either side. If one is Drawn to the Dark Side by anger or fear, it will amplify said quality in them. The same could be said about the light.
Since West End Game's Star Wars RPG, Force abilities have fallen into three primary disciplines: Control, Sense and Alter.
Control powers focus on controlling the user's body (and the body of others for more skilled users). It's largely buffs.
- (Jedi) Meditation (Trance): Sends the user into a deep sleep that boosts the speed they recover from wounds and fatigue while also using less food and air than normal waking or sleeping. On the downside, it's a really deep sleep, so the user will only be woken by physical stimulus, a code word that terminates the trance is heard or a pre-selected amount of time elapsing.
- Force Speed: Speeds the user up and/or greatly slows their perception of time. Combined with foresight it allows blocking blaster bolts. Combined with telekinesis it allows the user to make very large leaps.
- Mind Trick: If the target is a weak-minded individual (typically one of the obedient goons working for the BBEG), a force user can employ a "Jedi Mind Trick" to confuse and misdirect said individual. Despite sounding somewhat nefarious ability for a light-side user to have, most of the time they just employ it as a "leave me the fuck alone and forget I ever existed" card. Some species are naturally immune to the Mind Trick, though.
As you'd expect, Sense holds all the divination powers. Also Telepathy.
- Foresight: The most common force power, and only one that is used unconsciously by untrained users. It gives the user glimpses into the future, which at the lowest level gives the very practical ability to react to things before they happen. At the highest level it gives visions of the long term future, though these visions tend to be pretty useless since they're vague and attempts to prevent them nearly always result in them coming true.
- Farsight: Allows the user to see things happening elsewhere. This sometimes translates to feeling major fluctuations in The Force, especially when it involves mass-genocide of entire planets or of the Jedi Order.
Alter is the broadest category and holds powers that alter the world around the user. In practice this works out to anything not covered by the above two schools.
- Telekinesis: Control stuff with your mind! Easily the force power with the most variants. In addition to the many abilities to move specific things in specific ways, it's also the basis of some odd-ball powers like starting fires by agitating particles enough till a fire starts. Used on the user, it allows them to leap great distances. Used on the enemy, it can crush their vital organs, throw them into pits or throw heavy stuff at them. In virtually everything except the original WEG material, using telekinesis offensively (outside of force choke) is not considered a dark side act.
- Energy Projection: Most commonly encountered in Force Lightning, this power allows the user to fire off energy as an attack. Generally dark side when used against living things. A handful of sources feature a variant that pulls the energy of an opponent away from them, disabling them non-lethally and thus not a dark side power, but it's often considered Skub. Another non-dark variant occasionally seen in RPGs is a variant that only works on droids, but nobody really care about this (outside of maybe Clone Wars campaigns) because it's completely useless when fighting anything other than droids.
- Immortality: aka "Force Ghosts." Only a select number of Jedi have ever learned the secret of retaining their souls upon death so they can communicate with the living, rather than simply return to the Force. Qui-Gon Jinn discovered the technique, then posthumously passed it on to Yoda, then to Obi-Wan, and then the Skywalkers. As Obi-Wan put it, death, quite the opposite of setback, makes one "more powerful than you could possibly imagine." This ability is limited only those who commit themselves to the Light Side; while the Sith have also sought out immortality, they're limited to transferring their souls from one vessel to another, or else living a more wraith-like existence, bound to a place or object by their malice and hatred.
The most famous users of The Force in the Star Wars franchise is The Jedi Order, a semi-monastic order dedicated to keeping the peace in the galaxy. An ancient schism led to some Jedi leaving the Order and turning to the Dark Side, and they created the Sith Order. Jedi who fall to the dark side without becoming part of the Sith, and certain non-Sith trained by Sith in the force become "Dark Jedi", but this term is often applied to independent dark side users who have never had an affiliation with the Jedi order.
The general term for a force user that isn't part of of the Jedi or Sith is Force Adept. This term was invented whole cloth by Wizards of the Coast and sees little official use outside of RPG products, though the fandom likes it. A more widespread but blander alternative is simply "force user". "Darksider" is often used as a general term for dark side force users.