Redshift space is the configuration of space we see taking the redshift of galaxies and other distant bodies as the radial dimension (considering the space in spherical coordinates), as found in redshift surveys. The representation of data such as this in three dimensions is termed a data cube.
Redshift space's exploration is used to determine geometry of the universe over time, e.g., the accelerating expansion, or dark energy.
Redshift space is a distortion of "true" space (redshift space distortion or RSD) when the peculiar velocity of galaxies affects their redshift, e.g., in an region where galaxies have high random peculiar velocities (appearing stretched toward and away from us, i.e., the finger of God distortion) or a pattern of high peculiar velocities (e.g., when they are attracted toward the center of a larger structure, the Kaiser distortion). The Alcock-Paczyński effect also presents complications.