Well, the first thing you'll want to remember about the title is that it's "The Waste Land," and not "The Wasteland." A silly distinction, maybe, but it's not an exaggeration to say that more than half of students usually get this title wrong on tests or essays, since computer autocorrect will try to make it one word. Stinkin' autocorrect.
On a symbolic level, "The Waste Land" refers to the spiritual and intellectual decay of the modern world. Throughout the poem, the image of a waste land shows us that, according to Eliot, 20th-century culture is just a barren, desert-like world with no real redeeming qualities, like, at all. Most importantly, the waste land is infertile, and therefore incapable of letting anything grow. This infertility symbolizes the spiritual and intellectual death that has happened in modern society, where it is impossible for any new hope of faith to grow—or any good art either.
This symbolic landscape pops up at several early points in the poem, but it is mostly represented by the "arid plain" of "What the Thunder Said." In this section, you really get a sense of the "mountains of rock without water" (334) that Eliot has been talking about since as early as line 24: "And the dry stone no sound of water." This landscape is sometimes substituted with other unpleasant places, like where the speaker sits beside the Thames River and watches a rat "Dragging its slimy belly on the bank" (189). But for the most part, "The Waste Land" usually refers to a dry, barren place that is swept by harsh wind and constantly shaken by "dry sterile thunder without rain" (342). No water, no good art, no nothing.
The speaker sees himself as a lone figured wandering across this waste land, picking up and sifting through the broken fragments of a culture that was once awesome and is now like Las Vegas on a Sunday morning. Throughout his travels, he picks up bits of Greek myth, Shakespeare, Dante, Wagner, and medieval English legend in order to try and make sense of his predicament. But none of these fragments are enough. He continues to thirst for spiritual renewal in a land that seems destined to remain dry.