So your image now has a colour gamut. Guess what - your monitor has one too! It can only display certain colours. It's not much of a problem though. Monitors can display most if not all of the colours out of both sRGB and Adobe RGB for it to be a non-issue. Some monitors have settings so they can display the whole sRGB gamut, and some even the Adobe RGB gamut. As long as your monitor is properly calibrated so that the colours that it displays are accurate, then you don't need to worry too much about the gamut of the monitor. Do note though that as monitors age, they can wear out. Particularly with CRT monitors, the amount of colours that it can display gets reduced. It might be that the monitor can no longer display the differences in the darker shades. You've then got a reduced gamut, and for accurate editing it would be beneficial to replace your monitor.

The final colour gamut is the gamut of your printer. This can be where the problem is when you're trying to get an exact colour match. Most colours are fine until you get into the very saturated colours. The stronger reds, greens and blues are the colours which cannot always be printed.