To attach a particular quality to something is to consider it to have that quality.

I don't attach any importance/significance to these rumours. 我不把这些谣传当回事儿。

She attaches great value to being financially independent. 她特别看重经济独立。

If you say that a particular quality attaches to someone or something, you mean that they have that quality.

Don't worry - it was an accident and no blame attaches to either of you. 别担心——这纯属意外，谁也不会怪罪你们俩。

[ + -ing verb ] Great honour attaches to winning this award. 获得该奖是莫大的荣誉。

If you attach yourself to a person or group, you join him, her, or it, usually for a limited period of time.

Being on his own, he attached himself to a noisy group at the bar. 因为就一个人，他跟酒吧里一群闹哄哄的人搭上了话。