Explanation of the above incantation (RewriteRule):
^(.*)$ -- the kind of files you want redirected, in this case, all files (from the root of you domain) as indicated by the dot and asterisk enclosed in parenthesis. The caret (^) and dollar symbols signify the beginning and end of your rule. Additionally, the file that is being accessed is automatically saved into a variable.
http://forum.new-domain.com/$1 -- the URL that it is being redirected into. The $1 is the first variable that was saved by the program which was the first occurence of a parenthesized regular expression (in this instance the "(.*)".
[R=301,L] -- Flags used to tell apache that it is a permanent redirection (R=301). L tells apache that it is the last rule.