Twitter has come up with a nice little function that allows any of your followers to send you a DM (Direct Message) without you having to follow them back, which is a very sensible move. The default for this option has been set to off, so you have to enable it. If you want to do it, it's very simple:
Go to your Twitter settings, and scroll down. You'll see this:
Simply tick the 'Receive direct messages from any follower' and you're good to go.