Plain English Meaning
It's the older FAA approval standard that says a GPS unit is good enough to be used for IFR flying. A GPS built to this standard can be used for navigation in the clouds, but it has to check its own accuracy and isn't WAAS-capable on its own.
Full Definition
TSO-C129 is an FAA Technical Standard Order that sets the minimum performance standards for stand-alone GPS receivers used as a supplemental means of navigation under IFR. Equipment certified to TSO-C129 (or its update, TSO-C129a) requires the receiver to perform receiver autonomous integrity monitoring (RAIM) and was the original certification basis for IFR-approved GPS units before the introduction of WAAS-capable receivers certified under /C146.