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 (presumeably) within their skull, the neccesary nutrients would be extracted from the said subsatnce, and the pure water woul 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 gargoyle has mastered the valuable talent of closing its mouth, 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.
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.
The Ankh-Morpork City Watch has the gargoyle constables Downspout (Feet of Clay) and Pediment (Jingo); 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. A gargoyle's natural way of life is to sit on roofs and sieve rainwater through their ears and mouth to strain for gnats. Gargoyles' preferred food is pigeon; the Watch gargoyles are paid in pigeons.
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...