In Greek Mythology
Thanatos was the son of Nyx and Erebus and the twin brother of Hypnos (sleep). As the embodiment of death, Thanatos was seen as a hateful figure, detested by men and gods alike. He dwelled in the Greek underworld, notably Tartarus, and was depicted in contemporaneous art as a winged youth. His Roman equivalent was Mors.
The Wiles of Sisyphus
When Sisyphus, the wicked king of Corinth, betrayed Zeus, the god ordered Thanatos to bind Sisyphus by chains in Tartarus. However, the sly Sisyphus managed to bind Thanatos in the chains instead and all death came to a halt. This bothered Ares, god of war, whose lust for battle could not be satiated with armies of immortal warriors. Ares would then personally travel to Tartarus to free Thanatos and seal Sisyphus to his fate. But again, Sisyphus would try and cheat death by claiming to Persephone that his earthly body was not given a proper burial by his wife. Persephone pitied him and allowed him the right to return to the world above but before long he was dragged back to Tartarus by Hermes. Thanatos is sometimes seen as a branching off of certain aspects of Hermes.
In Persona 3
One of the more powerful persona in Persona 3. Thanatos is the highest-leveled persona of the Death Arcana.
Thanatos first appears in the game when Minato summons Orpheus for the first time. At the same time, he awakened Thanatos, who also resided unknowingly within his psyche. His appearance caused the "death" of Orpheus, cutting off his head as he brutally emerged from within Orpheus.
After Thanatos vanquished all the shadows, he disappeared, and Orpheus regained his original form. It is revealed later on in the game that Ryoji is the equivalent of Death. Aigis's mission was to defeat Death, but failed to do so. Instead, she sealed Death inside Minato, who happened to be in the area of the incident. Having been sealed inside Minato for ten years, Death gained human traits like physical appearance and emotions and feelings. But at the same time, Minato was able to "copy" Thanatos from Death and made it available to summon him as a persona in battle.
Ryoji then reveals to the main character his true form, which happens to be identical to Thanatos. Here, the player has to decide either to kill him or let him live. Killing him triggers the bad ending, while letting him live extends the game to January 31st and gives the player a chance to defeat Nyx and trigger the good ending.
Thanatos can be obtained later in the game when the Death Social Link reaches its maximum level. By fusing certain personae, he can be created. Thanatos can also be fused with Orpheus to create Messiah, who is considered the main character's ultimate persona.