Responsibility (noun)

1. The state or fact of having a duty to deal with something or of having control over someone.
2. An obligation or accountability for something within one's power, control or management.

Origin:

Late middle english: from old french responsabilite, from late latin responsabilitas, from respons- "responded", from the verb respondere.

Examples:

1. He took responsibility for his actions.
2. She accepted responsibility for the project.
3. The company took responsibility for the environmental impact of its operations.
4. The parent has the responsibility of raising the child.
5. The manager has the responsibility of leading the team.