You should activate HTTPS and Privacy feature on Facebook if you concern about security. Please follow instructions below to accomplish it.
Open your account setting, go to https://www.facebook.com/editaccount.php or by accessing Accounts -> Account Settings.
On Account security check Browse Facebook on a secure connection (https) whenever possible. Your connection to Facebook will use secure HTTPS whenever posible.
Check When a new computer or mobile device logs into this account: if you want be notified if somebody else access your account from diferent device. Click save.
Next, go to https://www.facebook.com/settings/?tab=privacy, you may set your appearance on Facebook network. Its better if your account not open to everyone, so you have more control to whom your account may appear.