这是动词短语dreamed of的叠用，第一个dreamed之后省略了of。句意：在他年轻的时候，哈利一直梦想着某个不知名的亲戚会来把他带走，但这却从来没有发生过。动词（短语）叠用常表示“不停地/反复地/一直地做某事”。又如：

I waited and waited but my fishing rod stood still. 我等了又等,但是我的钓竿依然没有动静。

She ran and ran until she was blue in the face.她跑啊跑啊，直到脸色发青才停下来。

He thought and thought about it and still reckoned it wasn't worth it.他合计来合计去还是觉得不划算。