Civil aviation is one of the two major categories of flying, the other being represented by army aviation. Civil aviation refers to and includes all non-military aviation, meaning both commercial and private flying; basically, it refers to public use flights concerning citizens, individuals, corporations, companies and so on. Most countries in the world adhere to an organization that strives to create a standardized regulation for all of them to follow, for a better understanding and better overseeing of all flight operations and activity. This is the International Civil Aviation Organization and in 2011 it had 191 member countries, 190 of which come from the 193 members of the United Nations. The only countries from the UN that have not yet adhered to it are Liechtenstein, Dominica and Tuvalu; the 191st country pertaining to ICAO is the Cook Islands.
There are two major categories that can divide the civil aviation: general aviation and scheduled air transport; the latter refers to all passenger and cargo flights that operate within scheduled routes, whereas general aviation represents all civil flights, both commercial and private. Scheduled air transport is a much larger operation of civil aviation at least where the number of passengers is concerned, but general aviation has many more flights and flight hours as well, at least in the United States. General aviation actually transports more that 166 million passengers every year; that number is bigger than an individual airline, but much smaller than all of the airlines’ numbers combined.
Though most countries where civil aviation is present adhere to ICAO, some countries wish to make a distinction between commercial and private aviation, depending on whether the aircrafts used are flown for hire. For example, in commercial aviation most of the flying is executed for hire, especially within the scheduled service of airlines. On the other hand, private aviation refers to pilots that fly for personal purposes, whether for pleasure or business; these pilots receive no remuneration because they are flying their own aircrafts.
Another quirk of civil aviation is that, while all air transport that is scheduled is commercial, general aviation can be private and/or commercial. For commercial purposes, the pilot, operator and aircraft must have separate authorizations for commercial operations. These authorizations are obtained separately through commercial registration and licensing and operation certificates. As you can see, civil aviation represents most of the aspects of flight, excluding military or covert operations that might pertain to national security.