If Mail.app can't connect to your POP3-server(s) for some reason (ie you don't have an internet connection), it puts the account(s) off-line and shows this by displaying the tilde (lightning?) graphic next to the accont name in the Mailboxes drawer.
Did you know that clicking the off-line icon next to an account brings it on-line again, and likewise clicking the icon next to the In-box brings all accounts on-line again? Provided, of course, you have reestablished your connection to the 'net ...
Mac OS X Hints
http://hints.macworld.com/article.php?story=20040204062228210