my variables are statically bound.

sub test_a {
   my $var = "Hello World\n";
}

sub test_b {
   print($var);  # XXX Doesn't print Hello World.
}

test_a();
print($var);  # Doesn't print Hello World.
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local variables are dynamically bound.

sub test_a {
   local $var = "Hello World\n";
}

sub test_b {
   print($var);  # Prints Hello World.
}

test_a();
print($var);  # Doesn't print Hello World.
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However, dynamic binding is rarely used, because its use leads to fragile software. In Perl, local is mostly used to assign a new value to a builtin global, while automatically restoring the global's value when the block is exited.

sub test {
   $_ = $_[0];
   s/([a-z])/uc($1)/eg;
   return $_;
}

foreach (qw(a b c)) {
   print(test($_), "\n");
}

$ perl script.pl
Modification of a read-only value attempted at script.pl line 3.
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It's trying to modify the constant 'a', since $_ is a reference to it. Fix:

sub test {
   local $_ = $_[0];
   s/([a-z])/uc($1)/eg;
   return $_;
}

foreach (qw(a b c)) {
   print(test($_), "\n");
}

$ perl script.pl
A
B
C
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