The reason that they succeeded was that they worked really h

这个从句是定语从句,即修饰前面名词的,“.的原因”（怎么样的一个原因-这里是成功的原因）
另外,还有why引导的定语从句,
why引导表示原因的定语从句,其先行词一般是reason.当主句主语是reason时,作主句表语的成分不能有because和because of .其结构一般为the reason why…is that… 或者 the reason that … is that…
如：He did not tell us the reason why he was late again.The reason why （ that）he didn't come is that he was ill.