The phrase data cube refers to a three-dimensional array of data points, i.e., values of some sort. It is analogous to a table, which is a two-dimensional array of data points. Printing a data cube on paper might be accomplished with a series of tables: in this case, tracing the data through either of two dimensions could be tracing across a column or row in the table, but tracing data through the third dimension requires looking at successive tables.
A table, for example, might be constructed with the height above sea level of grid points evenly spread on a rectangular plot of land. An example of a data cube might be temperature values at points in space evenly distributed throughout a room, e.g., at one centimeter intervals in each of the three dimensions.
The three dimensions may not be analogous. For example, in astronomy, two spatial dimensions across the celestial sphere are straight-forward to collect and represent, and often some other third dimension is used if the collected data consists of a series of values from that point. Wavelength or frequency is a useful third dimension for data from integral field spectrographs. Another useful dimension is redshift, for distant very objects such as distant galaxies. A third is a straight-forward interpretation of redshift: radial velocity, e.g., for targets within the Milky Way such as groups of clouds. In all these cases, the data cube is a natural way to store the raw or nearly-raw data.