The number may not be relevant for enums to be useful. For example I use them when listing configuration options. I have a configuration file that holds details such as background colour, text colour etc. I have some code that reads specific options from the config file, this will map the enum with the specific entry (typically via a - large - switch statement) This appears quite clumsy but the advantage is that in my code whenever I want to use the actual background colour I will have a call similar to the following:
This is, I believe, very readable in the code and obviously easy for the user to change the settings.
With enums you can also set the value which also has its uses, if you have a small set
of values enums can easily solve it for you. Take the three classic font styles, bold, italic and underline, these could be assigned the values of 1, 2 and 4. Now simple bit operators can be used to see if the style is bold and underline (1+4 =5 or in binary 001 + 100 = 101)
Their use is limited to your imagination...