In simple terms, common ancestry refers to group of organisms that are supposed to be the descendants of a common progenitor (parent, ancestor). Inevitably, the descendants of the same ancestor will share some or the other features with the ancestor itself as well as with other descendants.
All the options you gave are related to Darwin's theory of Common Ancestry.
Studying common ancestry is of special interests for evolutionary biologists as it helps understand many evolutionary tendencies of organisms. In fact, it is a belief that all organisms on earth have been originated from a common parent or ancestor. So option (C) “evolutionary relationships” is most important.
Even in the descendants of the same ancestor, there were minor variations (as offsprings of the same parents have). And after natural selection, only the ones with best features survived. Option (B) Natural Selection cannot be explained without common ancestry.
Option (A) talks about kingdoms of hierarchal taxon. The classification done is in line with theory of one descent as the division is based on common characters every organism in the group shares. And this classification is based on common ancestry.
Similarly, Option (D) having a common genus also means sharing common features that can be attributed to having a common ancestor.