The side or vicinity of something or someone; beside/nearby (a noun-like usage indicating position).
彼の傍らに長年付き添っている看護師がいる。
There is a nurse who has been by his side for many years.
机の傍らにカバンを置いてください。
Please put your bag beside the desk.
畑の傍らの小道を歩く。
I walk along the path beside the field.
While/at the same time as doing something; indicating that one action is performed alongside another (often written/formal).
彼は会社勤めの傍ら、小説を書いている。
He writes novels while working at a company.
農業の傍ら、地元の学校で教えている。
Alongside farming, he teaches at a local school.
音楽活動の傍ら、翻訳の仕事もしている。
Besides musical activities, he also does translation work.