What is the meaning of 背会?
背会 and 会背 are not the same.

背会 verb + result, memorize/recite it until you know it (by heart)

会背 auxiliary verb + verb, able to recite from memory

我还没背会这篇文章。

I still have not learned this essay by heart yet.

今天不背会这篇课文就不回家。

I won't go home until I've learned this text by heart today.