As a verb, concern means something is about or talks about a certain thing or person. It shows what the topic or subject is.
The book concerns history of art.
This law concerns all citizens.
Concern can mean an important topic or problem that people care about. It is often used when talking about things that need attention or action.
Environmental concerns grow every year.
Safety is a major concern here.
Concern can mean a person or thing that is important to you or that you think about a lot. Sometimes we say 'not my concern' to mean it is not my problem.
His family is his greatest concern.
The noise was not my concern.
In legal or technical language, concern can mean an organization or person responsible for a task or issue. This use is formal and often in law or business.
All concerns must comply with the new rules.
The insurance concern is responsible for claims.