They have done all they could "to help" him.为什么是"to help"?

目的状语

They have done all they could to help him.
这是一个定语从句,they could修饰前面的先行词all。可以这样看：
They have done all （they could） to help him
后面的不定式作目的状语。

to help him 是目的状语从句
They have done everything "to help" him.
They went to his house "to help" him.
What should we do to help him?

do something to do句式

是目的状语

动词不定式做目的状语 to help
例：we study hard to pass the exam.

help sb.do sth 的固定用法中,help后面用动词原形.
而你的这句话：
主语 they
谓语动词：have done现在完成时态
宾语（从句）all they could
to help him在这里应该是目的状语从句
翻译：他们已经做了他们所能做的一切去帮助他.

to do 为动词不定式，其代表的意思有：
表将要发生的动作：we are glad to go to cinema.
表示目的：To suceed, we have to work hard.
在这个句中我想应是第二个意思可理解为：
我帮助他，他们把能做的都做了。