Tamora is the Queen of the Goths turned Roman Empress. After Titus ritually sacrifices her eldest son, Tamora makes it her mission in life to make Titus and his family suffer. She accomplishes this through her good looks, sensuality, and ability to manipulate those around her.
When we first meet Tamora, she's a pretty sympathetic figure. As Queen of the Goths, she's been captured by Titus's Roman army and paraded through the streets of Rome like an animal (1.1). Soon after, she's forced to beg and plead with Titus for her eldest son's life. This does her no good because Titus insists that Alarbus be ritually sacrificed in order to "appease" the spirits of Titus's dead sons (1.1.1). So when Tamora announces that she's totally going to make Titus pay, we can't say that we blame her.
Things take a turn for Tamora when Saturninus (who tells us that Tamora is really hot) proposes to make her his new empress. How does Tamora respond? By promising she'll be a "handmaid" to Saturninus's desires if he puts her in a position of power. This tells us that Tamora is willing to do just about anything (if you catch our drift) to get the power she needs to destroy Titus Andronicus.
Just because Tamora marries Saturninus doesn't mean she's going to give up her super-secret and super-steamy relationship with Aaron. When Bassianus and Lavinia catch her and Aaron in the woods, they see her extramarital affair as a "detested" act.
Believe me, Queen, your swart Cimmerian
Doth make your honor of his body's hue,
Spotted, detested, and abominable (2.3.2)
What's interesting about Bassianus's attack is that it suggests Tamora's "honor" has been compromised not (merely) because she's cheating on her husband, but because she's cheating with a black man. Most of the characters see the fact that Aaron is a "barbarous Moor" as the main problem, and this becomes even more clear when Tamora gives birth to Aaron's dark-skinned child. Confronted by Tamora and Aaron's mixed-race child, Tamora's son Chiron (a rapist) is embarrassed and says, "I blush to think upon this ignomy" (4.2.9).
Regardless of whether or not audiences feel sorry for Tamora when Bassianus and Lavinia confront her in the woods with racially charged accusations, the empress loses our sympathy when she encourages her sons to rape Lavinia while she runs off to have a dalliance with Aaron: "Now will I hence to seek my lovely Moor, / And let my spleenful sons this trull [prostitute] deflower"(2.3.13). By this point, Tamora's sexuality is seen as just as dark and ugly as her desire for vengeance and willingness to go after Titus's family members.