Consider them moving masonry with a personality. To some, gargoyles are considered "urban trolls", because they are stone-based. Gargoyles may be very distantly related to trolls, if they are related at all. Trolls are large humanoid rocks with valuable minerals for blood vessels and neural networks. Gargoyles live well in Ankh-Morpork which is steamy and baking in summer, so their nervous system is very likely different from that of trolls (for an explanation, see trolls). Gargoyles have various, slightly monstrous shapes (just like the gargoyles you might see on really old-styled buildings), many with wings and claws, and all with a mouth that is shaped like a pipe that cannot be closed. Due to this pipe-shaped mouth, gargoyles have difficulties pronouncing consonants, and it takes some mental translation to understand their speech (see Men at Arms). Gargoyles are extremely good at sitting still for a long time and watching the goings-on, therefore excellent job candidates for stakeout Watchman or semaphore watcher (watching the signals on another semaphore tower and relaying it).
They originally took minerals from the water that they had access to as a living gutter feature- the water would enter via the ear, and then, in the complex U-shaped alimentary tract that exists (presumably) within their skull, the necessary nutrients would be extracted from the said substance, and the pure water would be excreted out of their mouth. In urban Ankh-Morpork, however, they soon found that pigeons were easier (and more chemically substantial) to eat than sewer water, and so they evolved to eat these. Their ears eventually became useless, and the only remains of the U-shaped tract is an abnormality in their digestive system, much like the human appendix. It has also been hinted that the newest generation of gargoyles have mastered the valuable talent of closing their mouths, allowing proper communications with humans (see The World of Poo)
They are not comfortable coming indoors, and will rarely descend lower than the first floor of a building. One of the few times any were ever seen on the ground was when the gargoyles fled the Unseen University when they sensed the coming of the Sourcerer.
The rise of the clacks industry has opened numerous employment opportunities for gargoyles, for whom sitting still and watching a single spot for hours on end is normal behavior which they're pleased to be paid for. Gargoyles are also employed at the Royal Art Museum where their job is analagous to that of closed-circuit cameras, watching every entrance in and out of the building for signs of suspicious activity - ie, Thieves' Guild members with painting-shaped bulges in their coats. Others have found similar employment at private homes of the wealthy, serving a dual purpose as both vigilant watchmen and decorative statuary; for a small extra fee, some will even hold shields bearing the employer's coat-of-arms as they crouch guard.
The Ankh-Morpork City Watch is known to employ the gargoyle constables Downspout (Feet of Clay) and Pediment (Jingo); several other gargoyles are likely to be on the force as well, as William de Worde spots quite a lot of them while under Watch surveillance in The Truth. The modern Watch is an organization with much camaraderie, but the gargoyle constables fit in less well because gargoyles like to sit on the top and edge of buildings, and get uneasy when they have to be indoors or go nearer ground level. The Watch gargoyles are paid in pigeons, a practice which caused a few unfortunate misunderstandings before the dispatcher switched from carrier-pigeons to clacks for communication.
As mentioned in Men at Arms, gargoyles' normal locations are inherently bound into their names, like a limpet. Take Cornice-overlooking-Broadway, a gargoyle who stands on a roof and watches Broad Way. Other gargoyles, such as Downspout or Pediment, however, do not have names constructed this way. Possibly this is because as Watchmen, they have no normal location? Or maybe they omit the location from their name to make them more easily understood by humans...