The poem is "Dover Beach," by Matthew Arnold, and is a well-loved and often-quoted piece. It is likely that Montag grabs the book at random, since he has not had time to read and comprehend every book in his collection, but it turns out to be very poignant, bringing one of the women to tears:
"'And we are here as on a darkling plain
Swept with confused alarms of struggle and flight,
Where ignorant armies clash by night.'"
(Arnold, "Dover Beach," Wikipedia)
These lines parallel the society of the novel, where people have no interest in larger events, and no knowledge except for what is taught in government-controlled schools and government-approved television. They have no perspective on the imminent war, and they have no thought or care for the "ignorant armies" clashing "by night." Their opinion on everything not television-related is "out of sight, out of mind," and this poem neatly encapsulates that thought process.