"Velocity variations" refers to changes or fluctuations in speed or pace. It means that the rate at which something or someone moves is not constant and can either speed up or slow down at different points.
[1] Most of the exoplanets currently known were discovered using indirect techniques — such as radial velocity variations of the host star, or the dip in brightness of the star caused by a transiting exoplanet. (sciencedaily.com)
Due to the close binary orbital interactions of the host star with Alpha Centauri A and Star B's own increased stellar activity during recent years, the astronomers were only able to detect the radial - velocity variations of host star B that were caused by the 3.236 - day orbit of the planet (with a semi-major axis of 0.04 AU) only after more than four and a half years of careful observation. (solstation.com)
The detected velocity variations were too small to be cause by a body orbiting star A, which is more massive (see HR 5544 on page 919). (solstation.com)