Variation Reduction implies reducing the standard deviation of the process so that the variation observed in the output can be reduced. It is one of the two ways in which Six Sigma helps in reducing defects. It is the preferred option if the spread of the process is greater than the tolerance (i.e. Control limits are outside the Specification Limits)
Mean Improvement implies shifting of the process average closer to the target value. It is one of the two ways in which Six Sigma helps in reducing defects. It is the preferred option if the process mean is not equal to the target value
An application oriented question on the topic can be seen below.
Review the answer provided by Mr. Vishwadeep Khatri, Founder CEO, Benchmark Six Sigma