The poem, "He ate and drank the precious words", is poem XXI from Dickinson's collection of poetry in "Book One: Life". The poem is about a man who, through the reading of a book, has become metaphorically drunk.
As a result of his intoxication, the man has been able to forget his problems, being poor and his fame has been forgotten. Therefore, the words of the text are so life changing that he, in a sense, has been reborn:
What liberty/A loosened spirit brings.
Based upon this, the title of the poem relates to the meaning of the poem in the sense that the "precious words" which the man read were, in all reality, precious for the man. The man was able to find a new life for himself through the words in the book: truly a precious gift through precious words.