This scene comes in Part 2, when Montag has a meltdown and reads from a book of poetry to his guests. He cannot control his need to share the content of the book, and so causes distress in his wife and very awkward reactions in the guests:
Mrs. Phelps was crying.
The others in the middle of the desert watched her crying grow very loud as her face squeezed itself out of shape. They sat, not touching her, bewildered by her display.
Montag felt himself turn and walk to the wall-slot and drop the book in through the brass notch to the waiting flames.
(Bradbury, Fahrenheit 451, Google Books)
The words of the poetry touch Mrs. Phelps, and she has a real emotional response that neither she or the others understand. Montag, realizing that he is standing on very thin ground, burns the book to show that he was simply making a point, or in keeping with Mildred's lie about being allowed to read to show the silliness of books. If he had not burned the book, the guests might have turned him in right then and there, destroying his chance to make a difference. Instead, he uses the book to evoke a response in his guests and then destroys it, knowing that they have been truly touched by the words inside; the purpose of the book here is finished, and it can do no more good, but immense harm if the guests do not see it destroyed.
Montag burned the book of poetry in the wall incinerator in his home because he was mad. After he read a poem to the ladies and Mrs. Phelps started crying, Mrs. Bowles raged out at him and called him nasty.