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
}
}