To be responsible for something — to bear responsibility for a task, role, or duty and see it through.
このプロジェクトの進行管理に責任を持つことになった。
I've been made responsible for managing the progress of this project.
親は子どもの教育に責任を持つべきだ。
Parents should take responsibility for their children's education.
チームリーダーとして結果に責任を持ちます。
As the team leader, I will take responsibility for the results.