Meta-information is information on the information held within a data set. If data were a journal article meta-information would be the abstract and conclusion. In its most idealisic form meta-information makes use of the metadata and the data to paint a human and machine readable summary.
If for example a data file contained 10 years of temperature records at specific point in the ocean, and the metadata identified this point, the meta information would describe the position, the record length, the mean temperature, the trend, variance, any anomalies detected either through automated processing or through human interpretation.