For a pictorial view of gamma see the Gamma Tutorial
Gamma (Plain old Gamma or Monitor Gamma)
Almost every computer monitor, from whatever manufacturer, has one thing in common. They all have a intensity to voltage response curve which is roughly a 2.5 power function. Don't be afraid, this just means that if you send your computer monitor a message that a certain pixel should have intensity equal to x, it will actually display a pixel which has intensity equal to x ^ 2.5 Because the range of voltages sent to the monitor is between 0 and 1, this means that the intensity value displayed will be less than what you wanted it to be. (0.5 ^ 2.5 = 0.177 for example) Monitors, then, are said to have a gamma of 2.5
Who decided that this phenomena should be called Gamma? I can't answer
that. I've been told it dates back to the early days of photography. For
more history see An
Explanation of Monitor Gamma - Robert Berger, Carnegie Mellon Univ.
The idea of system gamma, is the gamma correction that should be applied in the software to produce an accurate image on the monitor for a particular computer "system." By computer systems we mean everything from the software that is running (like Netscape) to the graphics cards installed, to the standard hardware on the motherboard. Different computers do different things and many "systems" have different configurations of all of the above things. Note that this does NOT include the gamma or gamma correction of the image file one is viewing. For File gamma, see below.
Also the human response to the light produced on a computer system is affected by the ambient light conditions in the room in which the computer resides. Personal taste also plays a role. Therefore an image that is displayed "accurately" in terms of what functions have been applied may not look the best to you, the person viewing the image.
One can determine the system gamma of a computer using various charts that show pictures of black and white dots (which look gray from a distance) and show other images that are really gray. (The Knoll Software Gamma control Panel can help you with this on a Macintosh. Similar things probably exist for PC's. On the web look at An Explanation of Monitor Gamma - Robert Berger, Carnegie Mellon Univ. )
Macintosh (an example - for more examples, see the Gamma Tutorial)
The Macintosh has built-in gamma correction of 1.4. This means that after the software sends the signal to the framebuffer, there are internal hardware corrections which will further process the signal, specifically by gamma correcting it another 1.4 - That is, the signal is raised to the 1/1.4. Therefore, to get full correction, the software itself should first adjust the signal by raising it to the 1/1.8 power. (2.5/1.4 = 1.8) Thus the system gamma on a Macintosh is 1.8.
Note some graphics cards in Macintoshes may have their own software to change the standard gamma. Photoshop 3.0 is now released with a gamma control panel from Knoll software which allows the user to change the system gamma of his Macintosh. The 1.8 standard is still accepted as the universal Mac System Gamma, but users should be aware that a Mac can be set differently.
Individual image files can have a gamma. This refers to the amount of gamma correction that has been done on the data in the image. If you scan a file in Photoshop and set the scanner gamma parameter to 1.8, then the image data generated will be the data scanned, raised to the (1/1.8) power. Since 1.8 happens to be equivalent to the Macintosh "System Gamma" the image should then display accurately on a Macintosh. If the image file has gamma correction of 2.5 then it would be overcorrected for display on standard Macintosh's.
When the data is saved, after being gamma corrected to 1.8, that gamma correction stays with the file. However, most file formats (GIF, JPEG) don't have anyway to tell a user the gamma correction that has already been applied to image data. Therefore, the user must guess and gamma correct until he is satisfied with how it looks. The Targa and PNG file formats do encode the exact gamma information, removing some of the guess work. The 3D modeling program, 3D Studio, actually takes advantage of this information!
Gamma correction, then, can be done on file data directly (the individual bits in the file are changed to reflect the correction). This is what is meant by the File Gamma or "gamma of a file." On the other hand gamma correction can be done as post processing on file data. In the latter case, the data in the file is unchanged, but between reading the file and displaying the data on your monitor, the data is gamma corrected for display purposes. Ideally, if one knows the File Gamma and their own System Gamma, they can determine the gamma correction needed (if any) to accurately display the file on their system.
More about software gamma correction