A Martian address is a source or destination IP address that apparently does not exist on Planet Earth and is, thus, invalid and/or non-routable. Martian packets were first mentioned in 1995 in RFC 1812, Requirements for IP Version 4 Routers.
Martian addresses may be accidentally created by a misconfigured system or they may be created in an IP spoofing exploit attempting to trick the receiving network into accepting the address. A hacker might create Martian addresses as a preliminary to conducting a denial of service (DoS) or man-in-the-middle (MitM) attack.
A Martian address can also be simply part of a pool of reserved addresses which IANA (Internet Assigned Numbers Authority) does not allow to be used ordinarily. An illegitimate IP address that falls into a set of IP addresses that have not been officially assigned to an entity by an internet registration institute is sometimes referred to as a bogon (from the word bogus).
Most networks filter for Martian addresses. As a result, the software rejects the address and Martian packets are dropped. On the other hand, IANA is constantly updating and assigning new address space, so an invalid IP address may someday have a destination on Earth, at which point it will cease being a Martian address.
Scott Morris explains why Martian packets never make it through the routing table.