This mission is identical to the ship's usual special mission (code 9), see there for details. For example, for a Federation player, this mission is Super Refit, for a Crystal this is Lay Web Mines.
This mission is intended for client programs that do not have explicit PHost support. If your client program does support PHost, it will most likely let you use the normal Mission 9 to do your special mission.
If your client program does not support PHost, this mission has two uses:
The first is to reduce some confusion when playing in a nonstandard-race game (i.e., the PlayerRace config option is used to redefine racial assignments). Rather than seeing the built-in mission names for their race (which may be incorrect since the player may be playing another race), you can simply modify the name of this extended mission in your copy of mission.ini to be consistent with your true special mission.
The second purpose of this extended mission is to allow all qualified ships to perform the special mission, not just those ships which are recognized by the client program as being able to perform the special mission. For example, the DOS Planets client program will not allow player #11 ships to perform the special mission (nominally Build Fighters) for ships without fighter bays. But if player #11 is playing race #10, he actually wants to perform the RGA mission which does not need fighter bays. The Special Mission extended mission allows you to perform his special mission even when the client program will not allow it.
The Special Mission extended mission can also be set using the extmission command.