Dimensionality reduction refers to various methods for transforming a high-dimensional space (i.e. with a lot of variables/features) into a low-dimensional one (a few variables/factors) while preserving some characteristics or structure of the data. In classical applications such methods are applied to one individual data set at a time.
Joint dimensionality reduction refers to the application to multiple data sets such that the resulting low dimensional space is the same for all data sets. Typically jDR methods are simply existing DR methods tweaked to apply jointly to multiple data sets.