The CEO gave them his word that no jobs would be cut this year.

gave 是动词 give 的过去式，意思是"给予、提供"。 them 是人称代词 they 的宾格形式，指代前文提到的对象，这里指"他们"。 his 是形容词性物主代词，指代"他的"。 word 本义是"单词、话语"，在这里特指"承诺、保证"。 gave his word 是一个固定搭配，意思是"作出承诺、保证"，强调以个人信誉担保的正式承诺。