Wouldn't you like a cup of coffee for a break?

wouldn't 是 would not 的缩写形式，would 是情态动词，表示委婉的建议或邀请。not 表示否定。 wouldn't you like... 是一种礼貌的邀请方式，字面意思是"你难道不想...吗？"，相当于中文的"要不要..."这种委婉表达。