Spam is unsolicited bulk email.
Unsolicited means that it was not requested by the recipient, explicitly or implicitly.
Bulk means that it is being sent to multiple recipients. There isn't a hard-and-fast numerical threshold (although obviously two is an absolute minimum).
Note that this definition is content-neutral, and deliberately so. Sometimes people try to define spam to be unsolicited commercial email, and certainly the most common examples try to look like commercial advertisements, but spam could be political, religious, or just plain nutty. This is often stated as "Spam is about consent, not content." Besides reflecting the often libertarian ethics of the Internet, this also deflects the criticism that blocking spam is suppressing freedom of expression.
Another reason that consent to receive email becomes an issue is that as Internet email currently works, recipients effectively pay for the ability to receive email, while senders pay little if anything to transmit mail to recipients. This means that the cost of unsolicited email is primarily borne by the recipient.