The teacher mercifully gave the students who were late with their homework an extra day.

mercifully 是形容词 merciful（仁慈的）加上副词后缀 -ly 构成的副词形式。merciful 来自名词 mercy（仁慈、宽恕），表示"出于仁慈地"或"宽厚地"。在这里描述老师以宽容的态度对待学生。