In the past news traveled mostly by word of mouth and it took days and sometimes weeks before a person would become aware of an occurrence on the other end of the world.

by 是介词，表示"通过某种方式"。 word 在这里指"话语、言辞"，而不是"单词"的意思。 of 是介词，表示所属关系或来源。 mouth 本义是"嘴巴"，这里指"口头表达"。 word of mouth 是固定短语，字面意思是"嘴里说出的话"，引申为"口头传播"的方式。