the sum of the different
cameras,
lenses and
accessories for a given camera brand.
Photographic systems are a typical concern of the professional photographer. A large system usually means great flexibility. Beginners in photography will usually concentrate on this or that feature in a given camera body, but it would probably be more useful to think in terms of the system.
As an example, let's consider the Nikon system: the camera bodies range from the plasticky, $300 beginner camera to the $3000 professional F5, to the tank-like F4. There are lenses in focal lenghts from 6 to 2000mm, and in some focal lengths you have up to three different (and specialized) lenses. The system includes very specialized remote controls, bellows, close-up lenses, various types of fancy strobe.
This is a system that will not let you down. It is expensive, but the good thing is that it comes in modules, and up to now Nikon has not changed the central point: the Nikon lens mount. Thanks to the Nikon lens mount, you can also access the vast used lens market.
Professional photographers in many cases use lenses that are more expensive than their camera body, and they also like to have more than one body on hand. The possibility of mixing and matching lenses is important to them. It is also very important to know that, should you need an extreme wideangle lens, it would be easy to buy it or to rent it. And what if you want to connect your camera to a microscope ?
In 35mm, the leading systems are Canon and Nikon. There are also Minolta, Contax and Leica (although I would say that Leica is not general purpose).
In 120, the system to which all the others are compared is Hasselblad. The others are Mamiya, Bronica and Pentax.
Proponents of various systems often engaged in holy wars. One leading motivation for holy wars is that, once you get into a system, you are pretty much stuck with it: you can't really mount a Nikon lens on a Canon body or viceversa (the truth is, it can be done, but it is an ugly hack).
And once you invested some thousand dollars in system X, you want to completely remove the nagging thought that maybe system Y would have been better for Andean elephant photography. That's how people turn into zealots.
How to choose one: the leading consideration is the application: what do you want to photograph ? If you have a very clear answer here (for example: birds) than you may have a very clear choice (in the case of birds, choose between Nikon and Canon: it is mostly a matter of taste).
Then (or maybe before) you have film format. 120, 135 or large format ?
And of course, there is money. Contax makes wonderful bodies, and they are stunningly expensive. And they don't really do more than a good Nikon body.