What is the Korean word for "rumor"?

The Korean word for "rumor" is 소문 (所聞), which is actually a relative clause meaning "that which (所) is heard (聞)" or "what is heard." Therefore, 所 can mean "place," but it can also mean "that which", which signals the start of a Chinese object noun or pronoun relative clause. Consider the following sentence:

兒(아)即(즉)歸(귀)以(이)所(소)聞(문)告(고)其(기)母(모) 

The boy (兒) immediately (即) returned (歸), taking (以) what [he] had heard (所聞) to tell (告) his (其) mother (母).

In the above sentence, 以 means "to take" and is part of an expression meaning "to take something and then do something with it." In Korean, the 以 translates as 가지다, so in Korean the sentence would translate as follows: 아이가 (兒) 즉시 (即) 돌아가서 (歸) 들린 것을 가지고 (以所聞) 그의 어머니에게 말했다 (告其母).

 Here is another example of 所 being used to signal an object clause:

子(자)所(소)答(답)非(비)我(아)所(소)問(문)也(야)()

What you answered (子所答) is not (非) what I asked (我所問也).

子 can mean "son" or "child," but it can also be used to mean "you." 所答 translates as "that which (所) was answered (答)"  or "what was answered," but since it was preceded here by the subject pronoun 子, the clause 子所答 translates as "what you answered." 我 means "I," and 所問 means "what was asked," but since 所問 was preceded by the subject pronoun 我, the clause 我所問 translates as "what I asked."

In English, the above sentence essentially means, "You did not reply to my question." In Korean, the above sentence translates as "당신이 (子) 대답한 것은 (所答) 내가 묻은 것은 아니다 (非我所聞也). The "非...也" combination translates into Korean as "아니다." A shortened expression is 答非所問 (답비소문), which literally means "the answer (答) is not (非) what (所) was asked (問)," but can be translated as "an irrelevant answer."

Notice that 소문 (所聞) and 소문 (所問) are both pronounced the same in Korean, but mean two completely different things, which is why it is important to be able to recognize the Chinese characters.