The most recent common ancestor is someone in your direct line that you have in "common" (related to), with someone else. Most recent refers to that person being the closest or "most recent" to you in generations.
The diagram on the right helps illustrate who would be the most recent common ancestor between me and my Uncle. My grandparents are my most recent common ancestor with my Uncle. It is not my mother because she isn't my Uncle's ancestor.
It is not my great grandparents because they are not the most recent ancestor.
There are various ways some companies show you your MCRA. Ancestry has "Through-Lines", WikiTree has "Relationship Trails" and FamilySearch has the Family Tree App that shows you people who are close by if they are on your tree on the FamilySearch website. NOTE: These programs offer information contributed by individual users and all lines should be verified with good sourcing.