Limbo, as it is referred to in the dream realm, is an expanse of infinite raw subconscious. It is the deepest anyone can travel into the mind. Limbo exists as a space that is not dreamed by any one individual, but is a shared space where any mind can make drastic alterations of any kind.
Dom explains that due to the strength of Yusuf's sedative, none of their team will be able to wake up by experiencing death within a dream. Instead, the sleeper will fall into Limbo, the very deepest level of the subconscious mind. If one dies and wakes in Limbo they could easily spend what seems like decades 'down there', getting 'lost' in the space, and eventually accepting it as reality until, as Eames puts it, their "Brains turn to scrambled eggs."
Since Limbo is a shared space with no designated dreamer it is possible for anyone to build an entire world, but still not recognize they are dreaming because, as Cobb says, they will "create and perceive simultaneously" with no understanding that they are constructing within a dream space.
Limbo can be entered by traveling deeper through the dream levels. After Fischer dies in the Mountain Dream, Cobb and Ariadne are able to enter Limbo by sleeping. The only reason this is possible is because, as Yusuf establishes earlier, the team cannot create more than three stable levels of dreams. Therefore, sleeping in Level 3 results in a sleeper dreaming themselves into Limbo. It should also be noted that manually entering Limbo allows a sleeper to retain the knowledge that they are dreaming, making it easier to avoid becoming 'lost' in Limbo.
A Totem is an object that is used to test if oneself is in one's own reality (dream or non-dream) and not in another person's dream. A Totem has a specially modified weight, balance, or feel in the real world but in a dream of someone who does not know it well, the characteristics of the totem will very likely be off. In order to protect its integrity, only the totem's owner should ever handle it. That way, the owner is able to tell whether or not they are in someone else's dream. In the owner's own dream world, the totem will feel correct. Any ordinary object which has been in some way modified to affect its balance, weight, or feel will work as a totem.
Extraction is the art of infiltrating the mind of any person to steal their secrets. Extraction works through a process called Dream-Sharing— manufacturing the world of the dream and bringing the subject into that world, which feels completely real as long as they are in it. Those who commit extraction are called Extractors.
Inception is the allegedly impossible task of implanting an idea in someone's mind via dream-sharing and making them think it is their own. However, as the movie progresses, it is proven that Inception is not impossible and has, in fact, been done successfully twice (both times by Dom Cobb).
Nonetheless, inception is a very difficult process. It requires dreamers to plant the idea in a dangerously deep layer of the Subject. This becomes the first difficulty of inception, as descending into a level so deep (three layers or more) creates highly unstable dream level. A way to solve the problem with unstable dreams is to use highly powerful sedatives, but such a powerful sedative makes escape by death in a dream impossible. Instead, death drops the dreamer in Limbo.
Another necessary component in inception is to have the Subject accept the idea with as little involvement from the dreamers as possible in presenting the idea to ensure the Subject cannot trace the origin of the idea. Part of this is to make the idea as simple and as personal as possible to ensure the idea remains. Emotionally-based reasons for the idea are generally used if the idea is one that the Subject would not accept in real life, as emotion trumps reason in human beings.
The Dream Extraction Unit (more commonly simply referred to as the DEU) is composed of a team of professional extraction teams. The difference between these extractors and the rogues is that what they do isn't illegal--in fact, the DEU is a government sponsored unit. They've been trained by military programs for the specific purpose of hunting down and arresting those involved in dream crime. They take on various different missions--some infiltrate illegal extraction teams, some use their extraction methods to gain information from terrorists and high-level criminals, others engage in global hunts for internationally infamous dream criminals. They're often closely associated with the CIA and operate under a cloak of secrecy.