The poems were originally published as stand-alone works, and only later combined in a series in 1943 (New York) and 1944 (London). Their original name was supposed to be "The Kensington Quartets," named after the speaker's time in the Kensington district of London. Eliot, though, probably thought that this might make the quartets sound too connected to his specific 'hood, since he was already tossing a lot of his own life into the poems.
Instead, our title is the "Four Quartets," which might at first have you saying "No duh, how many quartets do you think there'd be?" That number is significant, though. Just as the first four sections of Eliot's "The Waste Land" mirror the four ancient elements (air, earth, water, and fire), the four poems of "Four Quartets" match this same pattern. "Burnt Norton" is connected to air, "East Coker" to earth, "The Dry Salvages" to water, and "Little Gidding" to fire.
Further, the five-part structure of each of the "Four Quartets" shows how much Eliot wants his poetry that brings not only nature, but human life into some sort of harmony, even if he can only get this sort of harmony to exist in his poem. (Getting people on the street to act exactly as you want them down is a different question, and we here at Shmoop don't recommend it.)
Of course, this larger poem has four mini-titles, too. More specifically, "Burnt Norton" is named after a house and garden that were located in southwest England that Eliot visited and found to be a pretty awesome place to hang out. "East Coker" is the name of a small village in Somerset, England where some of Eliot's classy British ancestors came from. "The Dry Salvages" is named after a group of rocks off Cape Ann, Massachusetts (where Eliot lived as a child), and "Little Gidding" is named after an English chapel that Eliot took a really long walk to (like, really long) in 1927.
The personal significance of each of these places in the titles shows how much Eliot, through his speaker, wants to connect his personal experience to universal spiritual truths, and it hints that the poet is trying to get his readers to make similar connections between personal details and our greater relationship to heavy subjects like time, death, and religion to show that any of us could find our lives just as deep and meaningful as is suggested here. This, in turn, shows Eliot's unending effort to give a sense of meaningfulness to life during a time in history when traditional sources of spiritual meaning (religion and belief in human progress) weren't all that cool anymore. Instead, Eliot plants his flags firmly in the titles here, and we as readers take our long, but hopeful, cues from the biographical and symbolic importance of those references.