Assigning and Converting to Profiles
Assigning a profile to a set of colour data numbers is nothing more than embedding into the file a tag that specifies how the numbers must be interpreted.
In this context, the 'profile' could be a profile determined by the characteristics of a particular device, such as a printer, or it could be the unique colours-to-numbers match of a device independent colour space.
If, for example, you 'assign' AdobeRGB to a photo file, its data will be interpreted by any ICC aware software as representing AdobeRGB colours.
It should be clear from the earlier discussion that you should not 'assign' a colour space randomly: if you 'assign' sRGB to a photo-file where the numbers actually represent colours in the AdobeRGB colour space, the numbers will be interpreted as sRGB and the colours will be dull and flat.
The time to assign a profile, or colour space, is when:
Assigning a profile does not change the colour numbers. It simply declares how they should be interpreted.
Converting to a profile, on the other hand, does change the colour numbers.
Consider a photo-file that has AdobeRGB 'embedded' (this means that the numbers are to be interpreted as AdobeRGB colours and the file is 'tagged' accordingly.)
Suppose you wish to send this file to an output device that does not have a wide enough gamut to deal with AdobeRGB colours. You could first convert all the colour numbers to the sRGB numbers that represent the same colours, and embed into the file a tag that says to interpret the numbers as sRGB.
You typically always convert to sRGB when sending a photo-file for display on the web, because the sRGB colour space is the lowest common denominator space and you can be sure that most of the colours in your image can be seen as you saw them.
Whether or not they will be seen as you saw them depends on three things:
When you send a photofile to print either you, or the printer software, converts the image data from device-independent colour values, to the printer profile — the numbers that are needed to represent the colours of your image on the printer.