DISCLAIMER: This theory is old, it was conceived at a time when not much information was given on the subject. Furthermore, it is badly written and probably complete nonsense. In fact, after reading it again after years, i think only the last paragraph may actually make sense. Nevertheless, enjoy reading, but do not give it any serious second thought-
The Hougyoku (lit. Crumbling Orb, Shpere of Distortion) is an object which is able to "manifest The Heart" of anyone around it and therefore makes it possible for him to actualize his desires. Of course, there are a few restrictions to this nearly almighty ability: For his dreams to come true, the person in question has to possess the actual potential or "power" to realize them. Furthermore, it can only read the deepest of desires and aspirations, which naturally move the heart the most. Lastly, the user has to be in more or less direct vicinity of the Hougyoku for his emotions to be read. The power of the Hougyoku was originally thougt to be breaking down the barrier that separates the two contrary forms of existence, Shinigami and Hollow, and therefore the transmutation of the respective species into the other. However, this was only the case because it was the strong wish of the Hougyoku´s creator, Urahara Kisuke, and the reason for its development. Later, it was used by Urahara to create the Vizard, a hybrid species based on Shinigami with inner Hollows, and by Aizen Sousuke to create an army of Arrancar, Hollow who acquired a Shinigami-like appearance and a Zanpakutou. Furthermore, the Hougyoku is able to fuse with a being of excessive spiritual power such as Aizen. In this case, because of the stronger and direct connection of the Hougyoku and the wielders heart, the person will gain immortality and a massive increase in power, as his soul itself will be restructured numerous times in order to improve indefinitely according to the desires of his heart, even if they may be unconcious.
Based on other loosely related inventions of Urahara's, namely Gikongan and Gigai, I formulated a hypothesis of the nature of the functioning of the Hougyoku´s powers. For this, let´s first analyse the principle of Gikongan ("Artificial Soul Pill") itself in detail: The Gikongan is a small pill that, when ingested by a person, expels their spirit from the body (thus allowing Shinigami to leave their Gigai and fight more efficiently) and leaves an artificial soul behind to inhabit the body. It can also be used to animate an inanimate object like an artificial body (Gigai) or a simple doll. In each case, the pill links the pre-programmed conciousness of the artificial soul in the gikongan to the body and therefore allows it to gain control over it to move, speak and interact freely. How is this done? Normal spirits emit reiatsu (spiritual pressure) from their form, created by their reiryoku (spiritual power). The quality and intensity of the reiatsu emission depends on the composition and inner structure of the spirit in question, while shape and place of the emission can be manipulated at will to a certain degree (done so with Kidou). The Gikon takes this to yet another level as it can freely manipulate the place and intensity of his reiatsu emission, creating a 3-dimensional structure of "zones" of reiatsu: Meaning it can create reiatsu in any shape in a certain radius anywhere around it, though with very little strenght. Now, we know that spritrons do not mix very well with atoms. So, for a construct of reishi/spiritrons to interact with (have a physical effect on) normal matter, it has to possess a certain degree of density or pressure! So, when the gikon manifests a zone of high reiatsu at one point, it will influence the matter that is at this place, for example, activating a nerve, a muscle to move, etc. So, by creating different patterns of reiatsu, the Gikon can activate certain reactions in parts of an animate body, making it live, or push the parts of an object, making it move. In other words, the gigai acts as a medium for the soul, as it reflects it´s spiritual actions on the material world by binding it´s will to an actual object.
EDIT: We now know that the basic principle of a gikon (which was, in fact, invented by Hikifune and not Urahara!) is to take reiatsu from someone else and make it your own: She imbues her food with her own reiatsu to strenghten the spirits that eat it. Likewise, a gikon is filled with reiatsu from "sample-shinigamis", which contains their power and also their personalities. This reiatsu (scientifically amplified and "grown") then flows into another body and acts as their soul, strenghtening or animating it, creating a "clone" of the original reiatsu-donator.
Now, the Hogyoku can be seen as an extremely exceptional and excessively more powerful form of a gikongan: An artificial soul with no apparent will of itself (instead using the will of it´s wielder as the motive for it´s "actions") and the spirit of the wielder itself as a "body". The first, most important difference is that the Hougyoku isn´t a material object ingested by a material body, but a spirit-body made up of reishi itself. Also, the spirit doesn´t ingest the Hogyoku, but rather implants it into it´s own structure. Then, the orb doesn´t expel the soul/spirit of it´s user, as it doesn´t have the function of replacing the user´s soul with an pre-programmed mind, but it rather senses the "Will of The Heart" of the person wielding it and takes his intentions as it´s own mind. Then, just like a gikongan, it reflects those intentions on it´s medium, in this case, the body of the wielder, the soul itself (as we see here again, the main difference between a living being and a spirit seems to be that living creatures posses a soul inside of them that animates and controls the material body according to the soul´s wishes; whereas with a spirit, soul/mind and body are identical, and therefore, the form of a sprit directly reflects it´s personality and it´s will). In other words: The Hougyoku records the strong desires of the soul´s mind, and then directly manifests them on the soul´s body. For example: If the spirit wished to become stronger by gaining additional abilities, the Hougyoku will restructure the soul in a way that allows this ability, even if it originally wouldn´t have been possible for the soul to obtain such capabilities (a good example for this is the gaining of Hollow-powers). But: The wielder itself has to have the strenght to actualize his desire, the Hougyoku only removes the natural restrictions and limitations that would have hindered him from realizing it. It uses the reiryoku of the wielder, and therefore, it can not actualize anything that would require more reiryoku than the wielder posesses (On the other hand, by gaining new abilities, the user could in fact evolve into states of beings with more reiryoku). Additionally, unlike with a normal gikon, the medium of the Hogyoku, the field for it´s manifestation, is by no means bound to a single object, a body: With the Hogyoku, the field of the wielder´s reiatsu is greatly expanded, so that he is easily able to influence other beings or the surroundings: With enough power and control, the whole environment of the wielder acts as a "body" for him, and he can control it just like his own and manifest whatever he is desiring.
To sum things up, you could say that the term Hougyoku (Breakdown Sphere) really is a fitting denomination for this object, as it is able to break down the wall that separates mind and body, imagination and reality, inside and outside world, yin and yang; and allows one to realize what he is imagining. On the other hand, the opposite could just as well be true: The Hougyoku manipulating the conciousness of it´s wielder and therefore influencing him to do things... who knows!
How to create a Hougyoku? Aizen has been seen "offering the souls of thousand of spirits and Shinigami to his Hogyoku", but it just wasn't enough until he also gave Urahara's Hogyoku to it. So, what is the Hogyoku actually made of? Souls. Tons of Souls. Millions of Souls. If a Gikon is one single little soul compressed into the size of a pill, the Hougyoku is a whole population of souls mixed into an orb: While their individuality and consciousness got swept away in the stream of existences, their power and reiatsu added up or multiplied. The Hougyoku is an army of souls with individual abilities and powers, but all under the sovereignity/will of the wielder. If he gets wounded, he just summons a "spare soul" to heal or revive him. If he´s not strong enough by himself, he just borrows the power of some of the other souls. If he can't do something, he just combines abilities of other souls to get what he wants.