Peculiar velocity is the motion of an object with respect
to local rest. "Rest" depends upon observation and purpose.
For a star within a galaxy, "rest" might be taken as the mean
motion of nearby stars, i.e., how this star's movement differs
from the general motion of those around it. For distant galaxies,
e.g., in cosmology studies, "rest" might be taken as the motion
respect to the Hubble flow, i.e., the expected motion
away from us due to Hubble's law.