our makes a lexically scoped alias for a global. That means it remains in scope even if you change the package. Compare:

use strict;

package foo;
our $bar = 1;
# at this point, using $bar could mean TWO things:
# 1) try to access the global $foo::bar
# 2) try to access the alias named $bar for $foo::bar
# The lexical (second) one wins in perl, so you don't
# get a use strict error
print $bar;

package baz;
# Now $bar could mean:
# 1) try to access the global $baz::bar
# 2) try to access the alias named $bar for $foo::bar
# The lexical (second) one still wins.

print $bar; # works, prints $foo::bar even though we are in baz
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use strict;

package foo;
use vars qw/$bar/;

$bar = 1;
# $bar has only one meaning, access $foo::bar
print $bar;

package baz;
# $bar has only one meaning, access $baz::bar
print $bar; #error
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To answer the original question, the documentation is right, the our (as used in the first code fragment) has no effect outside the file. But... you can still access the global $foo::bar from another file. But this is NOT using the "our" alias as you can for example see by trying to do in that other file:

package foo;
print $bar;   # prints the global $foo::bar

package baz;
print $bar;   # prints the global $baz::bar
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