It means that if Alice sends a message to Bob, that message is encrypted with a key that only Bob (or Alice) knows. No server in between them can read the message, so the question of whether they trust the server doesn't matter very much.
Lavabit wasn't end to end encrypted. DarkMail will be.(Assuming it ever materializes)
Dark Mail is not End-to-End either. Last I looked, it had varying levels of security. The most practical one, from what I saw, is analogous to current SMTP+TLS. It gets the keys from the "organization" (aka gmail or your mail server). Given that it is incompatible with SMTP, I don't see the point. Use Gmail, add PGP if you need it.