Adobe RGB: Used when the output destination is a wide gamut (7+ inks) inkjet printer or a lithographic press (magazines, brochures, etc.).
The entire gamut of Adobe RGB can only be viewed on a wide gamut monitor and through a color managed application.
sRGB: For general viewing on normal monitors, for internet, for sharing with anybody unless you are sure they use a wide gamut monitor and c.m. programs, for commercial print labs.
There is a widely held false belief that Adobe RGB contains more colors. It doesn't. Both spaces have the theoretical capacity to render exactly the same number of colors (which is determined by bit depth, not space), but Adobe RGB spreads those colors out over a wider range. In practice, if you convert the Raw to Adobe RGB first and then later to sRGB, you will end up with fewer colors than if you converted the Raw directly to sRGB.