In RFI, "Focus" is a loose allagory for magic. It is wrapped up in a philosophical context that supposes that willpower is a fundamental force in the universe and some people are able to focus their willpower in such a way as to make inexplicable things happen, much like magic. It is, in fact, treated much the same as magic, with only a loose attempt to explain how it works, i.e. "it was willed to be so". This explaination coupled with the fact that it's rare allows for it's use to be more acceptable given the science fiction setting of the rest of the RFI universe. (That is, at least, the intention.)
The term "Focus" means an application of an entity's will in a directed manner, for the purpose of changing or influencing existence. It is also used to refer to the ability of an entity to perform such feats. (I.e. "He used Focus to levitate.")
Willpower is believed to be the most fundamental force in the universe. It is said that the reason for existence is that concentrations of willpower became dense enough to will themselves into existence. These pockets of willpower (called "jyse") eventually formed themselves into the first sentient being in the universe, who then guided the creation of existence as we know it.
These original beings, said to be Godlike in their powers, eventually faded, their willpower flowing into their creations and eventually draining themselves of their own existence. Some, it is believed, simply lost their powers, becoming the first mortal creatures.
The potential an entity has to focus its willpower enough to make an significant change to the universe varies widely with not just the entity, but also its race and nature. The vast majority of existence doesn't have the ability to use Focus; even among races like Humans it's astronomically rare for an individual to have the ability.
Every individual has different Focus-related talents. While they vary with the individual, they often follow the same underlying rules, so that, for example, two people who find they can manipulate time will find they have the same limitations as each other, and possibly manifest that manipulation in the exact same way.
Using Focus often (but not always) requires concentration on the user. When successful, the universe is altered in some fashion. It was explained by David Xenakis like this:
"Let's say you're looking for something you've lost. You know you saw it last night, and you're even pretty sure you remember what room you left it in. After searching high and low, you can't find it. What's worse is, you're going to be late, and you need whatever this is for whatever you're doing. You get frustrated, emotional and ready to scream at the universe until it listens and makes the object you want appear. Then, just as you were about to give up, you find it in the one place you kept thinking it had to be, despite the fact you've looked there two or three times already. Every Human's had this experience, but none of us knew what it meant. Talk to a Lyndri; they won't even understand your story. How can they? They've never experienced it; their race has no Focus users."
While there is some debate about the validity of his example, it does illustrate how a basic application of Focus can be used to do something as simple as change an item's location. A more advanced application could cause the object to fly to your hand, as opposed to appearing someplace unseen. This also illustrates a fundamental of Focus use; the more sentient creatures something affects, the more difficult it is to overcome their natural will for the universe to remain unaltered. This has the interesting effect that it's significantly easier to perform feats of Focus alone and unseen.
As with anything, there is a practical limit to how powerful a Focus user can be. They have an inborn total amount of willpower, and not matter how good the get at leveraging that, the are limited to whatever willpower they have. That is why some Focus users have experimented with ways to tap into alternative sources of willpower. These experiments are often disasterous, as the user finds themselves unable to maintain control as their wills are overridden by the more powerful willpower from the source they were 'borrowing' from.
All focus users have the basic ability to reshape the Universe in small ways, such as increasing their strength and speed, or healing injuries at an accelerated rate. Frequently, Focus users are found to age slowly, or sometimes not at all. Also common but not universal is the ability to move or teleport objects short distances. These are not seen as talents; rather they are simply accepted as part of what all Focus users can do. Instead, talents are the areas an entity's ability to Focus has manifested itself in interesting, but not entirely uncommon ways.
While minor teleportation of a non-sentient object a short distance is something most Focus users can do, teleportation of sentient entities (or objects containing them) is something only Focus users talented with teleportation can do. Theoretically, the only limit to this power is the amount of willpower the user can tap into; in reality anything more than self teleportation is difficult.
Often confused for teleportation, some Focus users have the ability to slow down (or speed up) time, allowing their reactions to seem impossibly fast, or making it appear as though they had teleported. This is often seen as easier than actual teleportation as (perhaps paradoxically) slowing down time locally is easier than willing a sentient being's location changed.
Some have studied the mechanism by which the Focus user actually slows time; it seems to be an advanced form of space-time manipulation, not unlike subspace technology. It is thought that because this is more akin to willing the formation of a storm than contesting the will of a sentient being, this is why time manipulation takes less effort than teleportation.
Some Focus users have been able to inflict injuries on foes that don't appear until the future; in rare instances, the Focus user can delay the impact indefinitely. This rare ability requires a huge amount of focus and the technique is rarely used.
Additionally, it's believed that some Focus users may be able to see the future; the quality of prediction is never perfect, however, since the entire idea of willpower requires free will, which means the future is always in motion.
While there are an unknown number of Focus using races in the Universe, the number in our Galaxy is rather small.
(See The Overseers for more information)
The Overseers are one of the ancient races known to be extremely gifted with Focus. All of their race has Focus abilities, though accourding to their legends that only came about after eons of dedication and advancement of their race.
(See Humans for more information)
Humans are known to have the potential to use Focus, though almost all of us are incapable of doing more than unconscious acts of manipulation. (And even that's debated.) One in every hundred trillion, however, has been known to have some level of ability; that so many humans (or near-humans) that can use Focus are alive and active at the time of the novel is a rare event, and most likely the cause of some of the problems. (And by the same token, probably part of the reason why a resolution was possible.)