To carry something on the shoulder or to shoulder/carry by lifting (physically bear on the shoulder).
祭りで若者たちが神輿を担って町を回った。
At the festival, young people shouldered the portable shrine and paraded through the town.
重い荷物を一人で肩に担った。
He carried the heavy luggage on his shoulder by himself.
子どもを肩に担って遊ぶ。
I carry my child on my shoulders and play with them.
To bear or take on a burden, responsibility, or duty; to shoulder (figurative responsibilities).
新しいプロジェクトでは彼が中心的役割を担っている。
He is taking on the central role in the new project.
社会は未来の世代の負担を担う必要がある。
Society needs to bear the burdens for future generations.
その会社は地域社会の期待を担っている。
That company carries the expectations of the local community.