Archaic: gradually; slowly — indicating that something proceeds step by step. In modern Japanese, 徐々に (jojo ni) is more common.
戦況は徐々に我方に有利となっていった（文語調）。
The course of the battle gradually became favorable to our side (literary tone).
気持ちは徐々に落ち着いてきた（現代語では『徐々に落ち着いてきた』が一般的）。
My feelings gradually calmed down (in modern Japanese, '徐々に落ち着いてきた' is typical).
Archaic: calm; composed; relaxed — describing a calm demeanor.
彼は何があっても徐々として動じない人物だった（古風な表現）。
No matter what happened, he was a person who stayed calm and composed (old-fashioned expression).