Position-position-velocity space (P-P-V Space or just PPV) is a conceptual space where two dimensions are the normal "space" dimensions and the third dimension is velocity. The concept applies to 3d sets of data (3d matrices, or data cube) where across two dimensions, the data applies to the two physical dimensions across the sky, and the third dimension applies to the radial velocity component of the movement of material seen along that line-of-sight. E.g., if along a line-of-sight, there is some material moving at 1km/sec away from the viewer and apparently even more material moving 2km/sec toward the viewer, then in that column within the cube, there would be two data points, with differing values in the V dimension, corresponding to those two radial velocities. There is a growing trend to store astronomical data, e.g., observations of clouds, in this format, e.g., for molecular clouds that include star-forming regions, in which internal structure is of high interest.
This is opposed to position-position-position space (P-P-P space or PPP) which is valuable when it can be determined.
The motivation for PPV space is: it represents the data that can be observed, the two spatial dimensions (e.g., based on astrometry) and the third, radial velocity dimension from spectrography (or the equivalent radio astronomy observations). Naturally it would be nice to have six dimensions, but the other positional and velocity dimensions can only be determined through less-reliable analysis, and PPV represents a less-interpreted, more reliable format. The more straight-forward analysis required to produce it is identifying Doppler shifted spectral lines, so as to detect the presence of gas moving at a given radial velocity.
PPV data is the natural result of an imaging spectrometer, or the equivalent radio observations. Position-velocity space (P-V space) similarly describes data resulting from similar analysis of a slit spectrograph, and position-position space (P-P space) represents just a normal image of the sky.