Certainly read the tutorials linked by AnonyMonk above.

Then consider the following code:

c:\@Work\Perl\monks>perl -le
"use warnings;
 use strict;
 ;;
 package P;
 ;;
 $P::A = 'something';
 ;;
 package main;
 ;;
 my $A = 123;
 $::A = 456;
 ;;
 print 'package ', __PACKAGE__;
 print qq{\$A is $A};
 print qq{\$::A is $::A};
 print qq{\$main::A is $main::A};
 print qq{\$P::A is $P::A};
 print qq{\n};
 ;;
 our $A;
 print 'package ', __PACKAGE__;
 print qq{\$A is $A};
 print qq{\$::A is $::A};
 print qq{\$main::A is $main::A};
 print qq{\$P::A is $P::A};
"
"our" variable $A masks earlier declaration in same scope at -e line 1
+.
package main
$A is 123
$::A is 456
$main::A is 456
$P::A is something

package main
$A is 456
$::A is 456
$main::A is 456
$P::A is something
[download]

In this code:

1. The package (or namespace) P is declared and the package variable $P::A is defined and initialized in it. This variable is autovivified by the assignment operation. strict is happy with this assignment because the package variable name is fully qualified.
2. The package (or namespace) is switched to main and a lexical variable $A is defined and initilized, and a package variable $main::A in the main namespace is defined and initialized. (The shorthand form of the fully qualified name $main::A is used.) The lexical variable is "visible" until the end of its lexical scope: the end of the program in this case although it might have been given a much narrower scope. The package variable is visible from any scope and any module; it is truly global.
3. The set of print statements shows that the lexical variable $A and the package variable $main::A (or $::A) are independently accessible.
4. The  our $A; statement is executed. our creates a lexical alias of the $A symbol to the package variable $main::A for the remainder of the lexical scope. I have taken this expression out of the print statement and made it a separate statement to more clearly illustrate how it works. The alias of the symbol $A to $main::A means that the original lexical variable (the my variable) named $A is no longer "visible", i.e., accessible. That's what the warning is about.
5. Another set of print statements identical to the first illustrates that $A is now indeed the same as $::A and $main::A.
6. In all the print statements, the $P::A variable is always fully accessible because it is always fully qualified.

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