Reading between the lines, it was obvious that something was wrong.

reading 是动词 read 的现在分词形式，read 的意思是"阅读"。 between 是介词，表示"在...之间"。 the 是定冠词，表示特指。 lines 是名词 line 的复数形式，line 在这里指"文字行"。 reading between the lines 是一个固定短语，字面意思是"阅读字里行间"，引申为"理解言外之意"或"领会隐含的意思"。