What does :: (double colon) mean in DOS batch files?

A line that start in double colon represent an invalid label that is ignored by the command processor, so it may be used to insert a comment. For reasons that can't be traced, many people use :: to insert comments in Batch files, but you must be aware that there are several pitfalls in its use that are described in the link given in Koterpillar's answer. It seems that the first use of :: instead of REM command was with the purpose to speed up the execution of Batch files in slow machines (ie: floppy disks), but that reason is not a valid justification for the use of double colon since many years ago.

Any line that contain an invalid label will be ignored by the command processor and you may use practically any special character to generate an invalid label. For example:

@echo off

:~ This is a comment
:` This is a comment
:! This is a comment
:@ This is a comment
:# This is a comment
:$ This is a comment
:% This is a comment
:^ This is a comment
:& This is a comment
:* This is a comment
:( This is a comment
:) This is a comment
:_ This is a comment
:- This is a comment
:+ This is a comment
:= This is a comment
:{ This is a comment
:} This is a comment
:[ This is a comment
:] This is a comment
:| This is a comment
:\ This is a comment
:: This is a comment
:; This is a comment
:" This is a comment
:' This is a comment
:< This is a comment
:> This is a comment
:, This is a comment
:. This is a comment
:? This is a comment
:/ This is a comment

echo OK

A line starting with a colon is a label which you can jump to with goto:

goto end
:end

A line starting with a double colon is a label, except you can't, even accidentally, jump to it:

goto :end REM this doesn't work
::end

Thus, double colon is used to comment lines out.

Source: http://www.robvanderwoude.com/comments.php

The colon (:) is a label marker and can be used for got instructions.

Some people use : as a comment too so a double colon is simply a stylistic REM statement