I want to change the colorscheme inside a vimscript like:
let g:scheme = "default"
colorscheme scheme
and i get the following error:
colorscheme "scheme" cannot be found
why is the variable 'scheme' not linked to the string 'default' when i execute the :colorscheme command ?
A "vimscript" or "viml script" or whatever (naming is hard) is really just a sequence of Ex commands, sometimes called "colon commands".
Most of those commands, like :colorscheme, only take straight up strings as input and don't even try to evaluate variables/expressions:
colorscheme scheme
In your example, scheme is treated as a string, not as a variable so, of course, you get an error because you don't have a colorscheme called scheme.
In those cases, which are relatively common, variables must be evaluated before being passed to the Ex command. This is done with :help :execute and the :help expr-.. operator:
execute 'colorscheme ' .. scheme