强调句：it is...that...= It is [被强调内容] that [其他部分]
It is 【that that "that"means that】(1) that contributs to [that](2).
先把(1)看做一个整体(事实上它是一个名词性从句)
It is (1) that contributes to (2).
意思是,是1对2有作用/帮助,或者说,促成2的就是1.
其中(2)=that很好理解,指代一件前面提到过的事情.
下面看1.
[一个知识]
有一类名词性从句是由that引导的,that后面说了一个完整的主谓齐全的句子,但是that + 这个句子一起,是具有名词属性的.最典型的就是宾语从句.诸如I think that.I believe that...等等.
这类that名词从句还可以做主语从句.比如：
That he is a good person is known by everyone.
(有时候我们让it做形式主语,而真正的主语就到后面去了,这只不过是为了避免头重脚轻的现象：It is known by everyone that he is a good person.)
下面看句子.that 为引导词.
that 【that "that"means that】,括号里的是真正的完整句子.
在这个句子：that "that" means that 中：
主语为：that "that"; 谓语：means；宾语that.
主语【that "that"】 前一个that是指示词,表示“那个”,后一个加了引号,意思是引用文字.主语说的是在某处出现的一个但词that.
而宾语的that又是一个指代,也是交谈的二人知道的.
于是主语从句【1】就是：【那个that意指的是那事儿】.
说正是【1】contributes了【2】.就这么简单.
全句再帮你翻译一遍：
It is 【that {that "that"means that}】 that conntributs to that.
译文：
【对此真正起作用的事情在于：彼处的"that"意味着那事.】