I think you are mixing up engine constants (the ones you see on the docs) with script constants (the ones you make on your own GDScript). They are not the same thing, in fact they must be different (you can't reassign a value to an engine constant).
The engine constants are predefined and made to be used with specific functions. For instance, you linked the doc page for RichTextLabel which has a function
push_align(int align). The argument must be an integer, so instead of doing
push_align(1) you do
push_align(ALIGN_CENTER) which does the same thing but it's easier to understand.
Now script constants you can define any value you want and use as you wish. So, recalling my example, if you have a
change_direction function that takes an integer value, you can do
change_direction(NORTH) instead of
Summing up, you don't assign values to existing constants (after all, they are constant), you just create new constants if you need them. Assigning a value to a new constant do nothing more than creating a constant with such value. As Zylann said, it's the same as a variable, except you can't change the value later.