Plain English Meaning
It is the FAA rule that says what a GPS receiver must be able to do before it can be approved for instrument flying. A GPS approved under this rule can be used in the clouds, but the aircraft must still carry traditional navigation equipment as a backup.
Full Definition
TSO C-129 is the FAA Technical Standard Order that sets the minimum performance standards for GPS receivers used as a supplemental means of navigation under instrument flight rules. A GPS unit certified to TSO C-129 may be used for IFR navigation provided the aircraft also carries, and the pilot monitors, the appropriate conventional navigation equipment required for the route or approach being flown.