The Bureau exists in the the spaces between worldstrands, in the noise of possibility that fails to cohere. It is something like an agency and something like an organism, with the least-flattering features of both. It is believed to prune possible worlds and digest them into noise in order to fuel its own growth, but leaves coherent clusters behind. There are theories about why it does this. Some say the Bureau is gardening, or pruning, engaged in some kind of meta-historical bonsai project -- or perhaps ikebana. Others believe the Bureau leaves these branches, woven threads of coherent possibility, in place as a concession to the system upon which it depends.
Another theory, less-popular than these, says that the Bureau excretes the worldstrands as a metabolic byproduct, the inevitable result of digesting so many other worlds. Objections that ingesting disordered things and excreting neatly-ordered ones is precisely the opposite of how digestion works are dealt with by the analogy of how purposeful dung looks to a beetle grub born therein (despite being waste shat out the backside of a wayward ungulate), or with recourse to causality-in-reverse, or not at all.
Seen from within, it resembles a nearly-endless office complex, ceremonial gathering, informal meeting of fellows, court, and nearly anything else that might stand in for the image of some group of people, more or less organized and gathered together for the purpose of getting stuff done according to the rules. There are sections that resemble a chess club match, a seasonal fishing ceremony, an illegal betting parlor, or BDSM dungeon. More than that, there are structures and working groups whose trappings and rules are related to none known, or only dimly connected to something in one's own history. The Bureau contains many people -- or at least they seem to be people, though none is completely independent from the Bureau as an entity. These people, along with the set decor and all of the interior contents, are believed to come from the possibility-threads that the Bureau digests, fragments of history incorporated directly into its structure. Those who have interacted with them often remark upon how normal they seem, and yet how utterly focused and fixated they are on their role within the Bureau. Some say they are its cells and active components; others, merely the atoms it has digested from its food. Biological analogies are always tempting, but ultimately fail to account for the details of the Bureau's organization.
Seen from without -- which you cannot do -- it might look like anything. It's probably got tentacles, because these things usually do. Perhaps it looks like a snowflake mixed with a spider, or a living breathing version of its own org chart (if such there be -- government and corporate analogies are also tempting, and no more reliably successful than biological ones), or some kind of vast celestial bovine wandering in a forest of worldstrands. You can imagine anything you like here, because you'll never find out anyway.
The only thing that's known for sure is that it can and does interact with worldstrands from time to time, including the individual threads of potential and history that we are generally a part of. In so doing, the Bureau can serve as a bridge between worlds.
Mostly, it watches. The Bureau seems to be interested in the goings-on of a world, from beginning to end, and no detail is too small or trivial to escape its interest. It can apparently watch a world from outside without obviously interfering in the course of events there (unless it should elect to nibble off the strand and swallow it). It is know to interfere and make changes in that flow, although its activities are typically subtle, usually a matter of rearranging contents by means of its agents. From time to time, it will engineer great changes in a world's course, although even then it does so in the subtlest of ways. Even the streams most spectacularly changed by the Bureau's interest are merely brushed, ever so lightly upon the surface, so as to allow its agents in.
It is sometimes suggested, albeit never very loudly, that She Who Meddles may be its servant.
Little can be said about its methods. It appears to whomever it likes, with purposes and motives that can only be guessed at. It is not usually whimsical or dangerous in its doings -- indeed, it can be relied upon to be explicit about its intentions to those with whom it treats, if not the greater context behind them, and it will always honor an agreement made in letter and spirit. It does have its own sense of what "spirit" means, though, and will tend to play by rules understandable to the other party. In that sense it serves as something of a mirror for one's own intentions. You will usually get as good as you give with the Bureau, unless it has decided you are part of its agenda whether you like it or not. Then you will find it impossible, in the end, to avoid its influence.
It has no names, not even "The Bureau" -- only an endless list of more-or-less polite referents, taken from any number of languages, cultures and social contexts. Usually it will present whatever aspect of itself seems to fit according to the perspectives and experiences of those it intends to deal with. This is believed to be a form of communication in itself, signalling its intentions and invoking the desired response in the contacted party. Agents and decor will present themselves accordingly.