I've received a "Getting back onto Facebook" email. I usually receive that email from Facebook when I enter a wrong password, but I'm sure this time it wasn't me!
What should I do now to keep my account safe?
Just enable login notifications. You'll be asked for a device name whenever you login. The name will be sent to your mobile (You have to activate facebook mobile for this). And once you name a device, like "Home",it won't ask again when you login from that device! Logging in from unnamed device always asks you this question. If you don't give a name,you'll get a message like,"an unknown device logged into your account at 15:30. Please change your password if it isn't you." Similarly,you'll get the message when you name a device like,"Home logged into your account at 18:00" but you'll get it only once!
To activate it,refer this!