The parents were beside themselves with worry when their child was late.

were 是 be 动词的过去式复数形式，表示"是"或"处于某种状态"。 beside 是介词，本义是"在旁边"，在这里与反身代词搭配使用构成固定短语。 themselves 是 they 的反身代词形式，指"他们自己"。 were beside themselves 是固定短语，字面意思是"在自己旁边"，实际表示"情绪失控、极度焦虑"的状态，形容父母因孩子迟到而非常担忧的样子。