Natural gas was originally thought of as a waste product of oil drilling. Soon, it was discovered that this gas (primarily CH4 -- Methane), was useful in its own right. Natural gas is an odorless, colorless gas (in consumer applications gas companies add a distinctive smell to allow for easier detection of gas leaks).
Natural gas is the cleanest of the fossil fuels. Combustion of natural gas produces CO2 (carbon dioxide, a common greenhouse gas also produced by all breathing things when they exhale), and H20 (typically in the form of water vapor aka steam). Natural gas produces far less air pollution than the combustion of coal, gasoline, heating oil, diesel, and most biofuels. Natural gas is provided by pipeline to homes and other buildings to heat water and for space heating where it is burned directly in a water heater or furnace (it is also used for cooking over an open natural gas flame). It is used to some extent in eletrical generation (primarily to handle peak demand loads) but is too expensive to use for baseline electrical energy generation. While most natural gas supplies used in the United States are North American in origin, there has recently been a push to increase the number of American port facilities that can handle imports of liquefied natural gas (LNG).
In a future hydrogen economy, natural gas will play a central role. Reformation of natural gas is the primary industrial means for the generation of hydrogen gas, which is envisioned for use in electricity generation in a fuel cell.
Like other fossil fuels, the supply of natural gas is finite, although "peak natural gas" (the point at which supply begins to decrease) is expected to come several years or decades after Peak Oil. As a result it is not a long term substitute for oil.
Heavier gases, such as ethane (C2H6) and propane (C3H8 are also used for similar purposes to methane (and indeed are a smaller part of the natural gas mix). Compressed natural gas is also used as a motor vehicle fuel, but with limited success -- as the infrastructure is not in place in cars or to fill up, and the long term incentive to use it as a replacement for declining supplies of oil are not there despite its "cleaner" nature. Simply put, a gas harder to deal with than a liquid and making a liquid out of something that is naturally a gas takes effort.