Acquired distinctiveness can refer to a few concepts in psychology. It can refer to traits that have been acquired or added to an individual's behavioral repertoire - anything from their basic appearance to talents or skills. You could say acquired distinctiveness is something that causes someone to "stand out in a crowd." An example of this would be a person who deliberately chooses to dress more formally and more expensively than their co-workers.
Acquired distinctiveness can also refer to a learned differentiation or ability to discriminate between qualities or traits that were initially indistinguishable. An example would be learning about wine-tasting and learning what differentiates the qualities of wines - before this skill was learned the person would be unable to discriminate between different types of wine. Acquired distinctiveness allows them to be able to distinguish between the wines. The opposing concept of this is acquired similarity