Data being stationary means that different parts of the data are effectively produced by the same underlying system, or come from the same probability distribution. If this is the case it implies that conclusions based on one part of the data can be safely applied to other parts of the data, since the properties of these data are essentially the same. This is important for analysis, and for training predictors of data, because successful training of the forecasting system depends first of all on the test (out of sample) data being stationary with respect to the training (within sample) data, and secondly on different parts of the training data being stationary with respect to each other.
DDM's stationarity test component computes relevant stationarity measures which take into account statistical properties as well as input-output relationships, effectively determining whether it is likely that the different parts of data were produced by the same underlying system.

