I'm not sure if you're referring to the city's cable cars or to its streetcars, as San Francisco has both. Let's start at the beginning:

Virtually every city in the developed world had horsecars in the 19th century. Those were horse- or mule-drawn vehicles that could seat a dozen or more people, sometimes two dozen. The steel wheels on steel rails reduced friction to the point that a single horse could pull a car full of passengers.

Local conditions, such as steep hills, sometimes presented problems for horsecars. After witnessing an accident where horses slipped on wet paving stones and were killed, Andrew Hallidie in 1869 developed the cable car (there were earlier experiments in Britain), with vehicles grabbing onto a moving cable under the street. The first line opened in San Francisco in 1873, and soon several other cities had cable car networks, notably Melbourne, Denver, and Chicago. The cable lines, powered by large steam engines in a central powerhouse, could propel cars with heavier loads than teams of horses could.

In the 1890s, the electrically powered streetcar, sometimes in North America called a trolley, proved practical and much less expensive than cable cars with their complex subsurface cabling, pulleys, and sheaves. Virtually all cable car systems had converted to electricity within a decade; Chicago’s last cable cars ran in 1906. Its hills made San Francisco an exception, though the dense city soon had dozens of electric streetcar routes, and the number of cable car lines fell from 23 to five. The cheaper new technology spread even to small cities, and by 1920 more than 800 cities in North America alone had electric streetcars.

The electric streetcar, in turn, was supplanted in most cities by motor buses from the 1920s to the 1950s. The buses were much cheaper to operate, were often viewed as more comfortable by patrons. But, again, they had difficulty handling San Francisco’s hills. After World War II, when buses had become powerful enough to replace the cable cars, San Francisco’s citizens rallied to save the unique transportation they had come to see as an emblem of the city. The remaining lines were pruned and combined into the three that still operate.

Meanwhile, electric streetcar lines had almost completely been replaced by buses around the world. Only seven North American cities still had streetcars in 1975—but one of them was San Francisco, due to two lengthy tunnels where ventilation for motor buses would be problematic. San Francisco began investing in its streetcar network in the late 1970s, building a Market Street subway and buying new vehicles. The streetcars were given segregated lanes wherever possible, with special boarding platforms, making the system more like a modern light rail system than traditional streetcar lines.

After a century of service and neglect, San Francisco's cable car system had to be shut down to be completely rebuilt between 1982 and 1984. Knowing that the “little cable cars” were a prime tourist activity, the city’s transit agency conceived of a Market Street Trolley Festival that would, during the cable car shutdown, run historic electric streetcars from around the world on the surface of Market Street from the Ferry Building to the Castro. The streetcars proved so popular that the program was retained even after cable cars returned to service, and the Market Street route was extended in 1995 to become the F Embarcadero line to Fishermans Wharf.

Today, San Francisco operates three cable car lines, the historic streetcars on the F line, and also a network of seven lines—much like those also found in Boston, Philadelphia, Pittsburgh, Cleveland, and Toronto—that can be called light rail. Since 1982, dozens of cities in North American and Europe have built new light rail systems, and about two dozen US cities have reintroduced traditional streetcar lines as well. But San Francisco’s cable cars remain unique.