It was October -when-- the People’s Republic\x0b of China wa

第一个句子：It was October when ...这里的 when 引导定语从句,修饰 October,全句直译是：那是中华人民共和国成立的十月.（当然,此句需要意译才会更通顺）.
第二个句子：It was in October that ...是一个 it was...that 的强调句型,它的陈述句是 The People's Republic of China was founded in October. 改成强调句型后不能漏掉陈述句中的任何一个成分,因此需要完整的状语 in October.