To Take Responsibility
To Assume Responsibility, To Take On A Burden
transitive verb, godan verb
担ぐ is more like when you're carrying something physical. 担う is when you carry a responsibility, which is why this word means to assume responsibility. You can remember this because YOU (う) are responsible for this. You assume this responsibility.
Note that 担う is generally used with another word that specifies the responsibility, like 役割を担う (assume a role) or 未来を担う (bear the future).
What is your responsibility? To raise this girl named Nina (にな).
地域を担う
to support the local community
業務を担う
to take on tasks
未来を担う
to bear the future
役割を担う
to assume a role
我が社の純利益は前年比で70％も上昇したが、それを達成するために私が重要な役割を担ったんだ。
My company’s profits soared 70% over last year and I played an important part in achieving that.