Did you enjoy the days that you spent in Beijing during the spring Festival? that you spent in Beijing during the spring Festival是定语从句，修饰先行词the days 。 that指代the days, 同时在从句中作动词spent的宾语。选择that是由从句中的谓语动词所决定的。试换一种说法： I enjoyed the days. I spent the days in Beijing during the spring Festival. 两句连起来就是： I enjoyed the days （that）I spent in Beijing during the spring Festival. 关系代词that在从句中作宾语，也可以省去。