What does the following code do?

This StatView::Script->new( ... ); calls the new method of the class.

The bit inside the parens:

{
    name          => 'stv_copy_key',
    version       => $VERSION,
    opt_spec      => [qw(
                            host=s
                            list_pollers
                            all_pollers
                    )],
    db_connection => [qw/ poller /],
    handler       => sub { StatView::CopySSHKey::run (@_) },
}
[download]

Constructs an anonymous hash which is passed into the new method.

It is equivalent to doing

my %hash = (
    name          => 'stv_copy_key',
    version       => $VERSION,
    opt_spec      => [qw(
                            host=s
                            list_pollers
                            all_pollers
                    )],
    db_connection => [qw/ poller /],
    handler       => sub { StatView::CopySSHKey::run (@_) },
);

StatView::Script->new( \%hash );
[download]

Are the keys mentioned predefined?

Presumably you mean the hash keys? If so, one assumes that they have some meaning to the class constructor, otherwise they would either raise an error or be ignored.

This:

is basically just syntactic sugar for:

with one key exception: in the first example, if the "Foo" package doesn't have a sub called "bar", then the object-oriented concept of inheritance is used to search for it in some other packages.

So in your example, the list of keys accepted by StatView::Script->new can probably be seen by examining the new sub in the StatView::Script package.

Foo::bar("Foo", $baz) what is Foo here. Is it a name of a routine or just a typical scalar value?

The first Foo is the name of a package, as in...

  package Foo;

  sub bar {
    print "Inside the package, I am called 'bar'\n";
    print "But outside the package, I am called Foo::bar\n";
  }
[download]

The second "Foo" is just a string scalar.

I really think you need to read perlboot from start to finish.

n Perl the constructor doesn't have to be named "new"

In Perl no, but OO frameworks like Moose and its derivatives have adopted this convention and use "new" for object instantiation.

Principle of Least Astonishment: Any language that doesn’t occasionally surprise the novice will pay for it by continually surprising the expert

Actually, constructors cannot be named new^†. The name of the constructor in Perl is called bless.

^†Unless you make an XS function called new which reimplements bless.

I thought a constructor is any routine that calls the bless operator.