What it was that he gave her was a lot of money. 

这个句子我估计是中国老师杜撰出来的，因为实际英语中很少有这样的句子。

英语中通过改变句子结构而强调某个句子成分通常有两种方法：分裂句（即强调句型）和假拟分裂句。

例如：我们想要强调He gave her a lot of money.这个句子中的宾语，可以：

1 分裂句：It was a lot of money that he gave her.

2 假拟分裂句：What he gave her was a lot of money. 

假拟分裂句中的what为特殊关系代词=the thing(s) which. 没有疑问含义。

还可以就分裂句中被强调的成分进行提问，构成特殊疑问句：

What was it that he gave her?

类似的就分裂句强调的不同成分提问的特殊疑问句模式如下：

What was it that?

When was it that...?

Why was it that...?

Who was it that...?

Where was it that...?

等等。

这种特殊问句还可以转变为名词性从句（去倒装、去问号），在主句中作动词或介词的宾语从句。注意此时的wh-词都是疑问代词和疑问副词，保留疑问含义。例如：

I asked/wondered/thought about/saw/understood/realized/remembered what it was that he gave her.

现在我们分析一下网友提供的句子：

What it was that he gave her was a lot of money. 

如果只看主语部分，这是由分裂句（强调句型）演变来的名词性从句，what应为疑问代词。但从系表结构来看，则句首的what又应该是特殊关系代词what（what=the thing which).。因此what的使用有不伦不类的感觉。其实这是将分裂句和假拟分裂句合并为同一个句子。

我个人认为，这个句子是一个病句，属于重复强调。类似于否定句中的重复否定：

I don't know nothing.

正确的强调方法是在分裂句和假拟分裂句中选择一种：

It was a lot of money that he gave her.

What he gave her was a lot of money.

A lot of money was what he gave her.

以上分析，共网友参考，也希望老师们指正。