Proper Motion of a star is its change in angular position over time, corrected for the Earth's orbit, measured in arcseconds per year. If you could measure the position of an object at two instances precisely one year apart, the angle in arcseconds between the two measured positions would be its proper motion. Proper motion is an indication of relative motion between the star and the Sun, but does not fully characterize it, which also requires knowing the distance to the star and the star's Radial Velocity.
Frank Ross's Catalog
Luyten Half-Second Catalog (LHS)
Max Wolf's Catalog of Stars With Proper Motion