The previous posts do go to the next line, the flag is set so that when you get to the next line, you know that the previous line was a match. If you get to a line, and the flag is set, then do whatever it is that you wanted to do after finding the matching line.
UPDATE-
I'm going to use tremmel's code to make sure that you understand what is going on, forgive me if I go in to too much detail, but I don't know where your level of understanding is - not trying to talk down to you, I'm a relative beginner myself.

my $flag = 0;
while (<FILE>) {   #If not at end of file process next line
    if ($flag) {   #flag is set, previous line was a match
        $flag = 0; #reset the flag
        do_something($_);  #do what you want to do after finding match
    }
    if (/pattern/) {  #if this line matches
        $flag = 1;  #set the flag so I can do something on next line
        next;  #go to next line, not required but might make more read
+able
    }
}
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