The Jyse are a race created through accidental experimentation by the Overseers. They were once jyse, pockets of willpower spread throughout the universe. However, thanks to the Overseers they were given physical form. Now they are obsessed with the physical world. Some long to rule, others to explore. But all long to exist in a physical form once more.
In many ways the story of the Jyse is a harrowing one. Even without physical form they are aware, with some of the most powerful able to subtly influence the physical world. But for the most part they are trapped in the fabric of the universe, aware, awake, and unable to communicate with anything, even one another. Their existence is an actual torture, but by their very nature they lack the ability to simply cease to be.
The Jyse race was created accidentally by the Overseers by channeling their will through jyse. Through their channeling, they found the jyse were able to respond, in a limited way, to how they were used. With much experimentation, the Overseers learned to communicate with the now semi-sentient jyse. Overseers adept in the use of Idrysi created Constructs to house some of the first Jyse. These newly formed beings became fully sentient. Their creation lead to the Jyse Wars that nearly ended the Overseers.
(For more details, see the Jyse Wars.)
After the Jyse were banished by the Overseers, they continued to be aware of the universe. Some were able to influence those sensitive to Focus use, able to communicate, or in rare instances even appear before them. Those who were powerful enough sought means to restore themselves back to the physical universe. So far, none have succeeded.
The closest is Sylvia, through the use of Jonathan Simon and is imperfect use of Idrysi.
Jyse are pockets of willpower, known by the common noun "jyse". However, as the pockets of willpower are fundamental to the existence of the Universe itself, despite how much will they have, they are unable to use Focus on their own. They must be given Idrysi Constructs that are created with the ability to Focus in order to be able to use it. This is why they cannot will themselves into existence.
It is possible, with enough willpower, a Jyse could manifest themselves in physical form, without the need for another. But that willpower would have to be so strong that it overrides the general will of the Universe keeping the Jyse as a jyse and not a physical being. While it's not impossible to imagine, it would take either an extraordinary amount of will, or a large number of powerful wills working together to achieve.
Once a Jyse is in a Idrysi Construct, they are, for all intents and purposes, a God. They are some of the most powerful Focus users in existence. The only thing they cannot do is continue their existence past the will of the Focus user willing them into being. As such, most Jyse became very protective of their Focus user, making sure that no harm befalls them.
Outside of a Idrysi Construct, however, there is very little they can do. Some are able to manifest themselves to particularly powerful Focus users, but even then the Focus user has to be unfortunate enough to attempt a channeling through them.
Jyse are solitary by nature; they would occasionally work in pairs, or small groups, but they were intensely individualistic, distrustful, arrogant, and short sighted. They saw no reason to work together, and instead pursued their own goals, often to the demise of others and, eventually, themselves.
The Jyse are important because Liz is a Jyse. Her story is the story of RFI; so her nature is important to the overall plot. That being said, the Jyse Wars and the fate of the Overseers is important to later stories, so the Jyse will make an appearance to more or less of a degree further down the line.
The Jyse were created while I was cramming all night for a Physics quiz, and one of my friends was keeping me entertained on the phone. He and I started discussing the nature of the universe, and this fledgling story I was working on, and he asked, "So if willpower is the most basic law of the universe, what happens if some of that willpower became sentient?" The rest, as they say, is history.