1. A method for filtering an email in a mobile terminal, the method comprising: setting a reading authority level in the mobile terminal, the reading authority level set to one of a plurality of reading authority levels, each of the plurality of reading authority levels indicating a different extent of the email that is displayable at the mobile terminal; receiving the email pushed from a push mail server, the email including a security level set, at an external terminal, to one of a plurality of security levels, each of the plurality of security levels indicating a different extent of the email that is displayable at the mobile terminal; checking the security level and the reading authority level in response to the received email, wherein the reading authority level has a higher priority than the security level such that any emails set with a security level are displayable at the mobile terminal when the reading authority level is set to a highest reading authority level; displaying the received email based on the security level and the reading authority level by: displaying all information of the email including a title, text, an attached file, and co-recipient information irrespective of the security level when the reading authority level is set to a first of the plurality of reading authority levels and when the security level is set to a first or highest security level that does not allow displaying of any information of the email or set to a second security level that does not allow displaying of the text, the attached file, and the co-recipient information; displaying the title and the text of the email by filtering the email if the reading authority level is set to a second of the plurality of reading authority levels even if the security level of the email is set to the first or second security level that does not allow displaying of the text of the email; and displaying the title of the email by filtering the email if the reading authority level is set to a third of the plurality of reading authority levels even if the security level of the email is set to the first security level that does not allow displaying of the title of the email; selectively deleting at least the title, the text, the attached file, or the co-recipient information of the received email set to the first security level such that the email is selectively displayable at the mobile terminal when the reading authority level is set to the second or third of the plurality of reading authority levels, wherein none of the title, the text, the attached file, and the co-recipient information of the received email that is set to the first security level is deleted when the reading authority level is set to the highest reading authority level; and setting a forward lock function to prevent forwarding of an email for which a security level is set such that the received email including the set security level cannot be forwarded to another email address unless the reading authority level is set to the highest reading authority level.