sRGB and AdobeRGB are two ways of selecting the ranges of possible colors that are to be included in the data that define your image.
You can go to Wikipedia for more -
http://en.wikipedia.org/wiki/Color_spaceFirst, "color space" refers to the range of "colors" that are being included in the data. Colors are just variations in electromagnetic energy that the human eye happens to be sensitive to and thus (short version) we see.
These can be measured along 3 dimensions, most commonly Hue (which could potentially (but not particularly usefully) go out into or beyond infrared or ultraviolet.
A second is Saturation or the purity of the color - how "muddy" or grayed out is it. Again, although math and specialized instruments can go way beyond what they eye can distinguish, the color spaces might possibly be extended various lengths along this dimension as well as Hue.
The third in what is known as the HSV model is Value, or brightness. Again, although they eye has limits, math and science can go beyond those nose numbers.
Oddly enough, no color space matches up perfectly to the limits of human vision, partly because that is a highly variable target, and mostly because it is not useful, since neither a paper print nor the priciest monitor can fully reproduce anything close.
sRGB was designed to map the range of colors that can be reproduced by monitors which rely on varying the brightness of Red Green and Blue phosphors to produce images.
Paper prints have far less range.
The Wiki article has graphs that illustrate some of these various color spaces and the eye's range (limited, of course, by the extent that the monitor can show these).
Digital cameras offer AdobeRGB since the sensors can record this wider range of values than the monitor (or paper) can reproduce, which is helpful if the original scene has that range in it. You can examine the histogram in the camera to see if using sRGB means you are losing data, but there is also a cost for mathematically recording the scene in a wider color space than the colors in that scene contain. There was a recent discussion of this at:
http://www.dl-c.com/board/viewtopic.php?f=4&t=40&sid=b5502efaba77b81867433fd899dd6f03uded by the numbers