Ever had a scary dream from which you couldn't wake up? Well, that's exactly the kind of setting Shakespeare creates in Titus Andronicus. The cycle of violence and revenge in the play is endless, and the world often seems like a nightmare, especially for the Andronicus family. At one point, Marcus looks upon Lavinia's mutilated body and declares, "If I do dream, would all my wealth would wake me! / If I do wake, some planet strike me down, / That I may slumber in eternal sleep!" (2.4.1).
It's also important to note that Titus Andronicus is set in ancient Rome, during the fictional reign of Saturninus. As critic Frank Kermode points out, the specific historical time frame is a bit of a mish-mash, because Shakespeare draws from various periods in Roman history to create the play's setting. But, as scholar Katharine Eisaman Maus notes, Shakespeare manages to create a general kind of "Rome-effect" by constantly alluding to themes from classical Roman texts like Ovid's Metamorphoses and Seneca's Thyestes.
Regardless of which century the play is supposed to be set in, we know that this isn’t the Roman world we associate with the height of civilization. Instead, Rome seems like it's on the brink of collapse, plagued by atrocities like cannibalism, rape, bodily mutilation, and ritual violence, which threaten to tear the city apart (literally and figuratively).
It's no wonder Titus calls Rome a "wilderness of tigers" (3.1.4). Just about everybody in the play is out for blood. Check out "Symbolism, Imagery, and Allegory" for more on this Rome as wilderness thing.