&{ $functions{$doit} };

Would be seen by Perl as:

"Take the value of $functions{$doit} and treat it as a sub name"

No, there's some confusion here about references. perlman:perlref is the definitive reference (no pun intended), but I'll try to give you the short answer.

The syntax &{ SOMETHING } is, as you correctly said, a dereference. It says "Treat SOMETHING as a code reference", which means that the subroutine referred to by SOMETHING is executed. That means that SOMETHING is taken to be a reference, and in the example given, that's just what it is, as is evidenced by the code:

my %functions = ('first'   =>  \&one,
    'second'  =>  \&two
);
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That \&one syntax is creating a hard reference to the subroutine one().

If, however that SOMETHING is not actually a hard reference, but is just a plain old scalar, then the "value of the scalar is taken to be the name of a variable, rather than a direct link to a (possibly) anonymous value." (from perlman:perlfref). So if the code example would have looked like this:

my %functions = ('first'   =>  'one',
    'second'  =>  'two'
);
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... then you would be using a symbolic reference, which is what you mean by "Take the value of $functions{$doit} and treat it as a sub name". NOTE that this whole Symbolic reference business is disallowed by use strict 'refs', meaning that our friend SOMETHING must be an actual reference, and not just a name. This is probably a Good Thing.

Hope this helps. And by the way, I think the syntax $coderef->() is preferable to the equivalent &{$coderef}, since I think it just looks clearer that you're calling a subroutine...