Mat 10:36 And a man's foes [shall be] those of his own household.

kai ("and") anthropos ("man") echthros (hated, enemy) autos (the same, themselves) oikiakos ("house member")

I show the complete phrase because it is nice and short and gives you a sense of how Greek in general is different, much more terse, that the English. In Greek of the Bible, the depth is not found in complex phrasing but within the choice of individual words.

"Foes" is not a noun, but an adjective, echthros, which means "hated" or "hateful." However, adjectives are frequently used to stand for a person or group with that trait. The use of echthros is very specific in Greek literature. It is one who was a friend, but who as been alienated and refuses to be reconciled. It is usually translated as "enemy" in the NT.

"They of his own household" is oikiakos, which means "one of a household." Households in Christ's time were not the temporary associations that they are today. It was the family you were born into, but it was broader than a family since it included everyone that worked together--masters and servants--in the family business. It combined our idea of a family with its idea of lifelong association with a small business where people were not necessarily related.

Christ is saying that his teaching will create divisions within this basic building block of society, that these livelong associations would be destroyed by the coming of his new philosophy.