sRGB vs Adobe RGB
If you're new or new-ish to photography, it's possible that you've stumbled across the term 'colour space' and the names 'sRGB' and 'Adobe RGB', but aren't entirely certain what they are and what their implications for your photos are.
This, then, is a very simple explanation.
Colour space
A colour space is a range, or gamut, of colours. Your printer can print a gamut of colours; your monitor can display a range of colours; and your camera can record a gamut of colours. Most cameras permit you to write images in two colour spaces: sRGB and Adobe RGB.
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sRGB
The sRGB colour space was developed by HP and Microsoft as a standard colour space for use on monitors and by printers. It's been around since 1996 and the vast majority of devices are calibrated to handle it.
Adobe RGB
The Adobe RGB colour space is slightly younger version, developed by Adobe in 1998. It enjoys a far wider gamut than the sRGB colour space and is designed to come closer to the CYMK colour space used in professional printing. In particular, it is capable of recording a greater degree of greens.
So I should use the Adobe RGB colour space, then?
It seems logical that bigger is better and you should be using the Adobe RGB colour space, yes? Well, not necessarily. You see, for the majority of instances where you are going to see or share photos, the gamut of the sRGB colour space is perfectly acceptable. When it comes to online sharing and the printers used for most photo printing, you'll find that they make use of the sRGB colour space. Unless it's likely that you might see you photos in book or magazine print, there's no real need to switch to Adobe RGB.