This is the ship of Humanity's Strongest Soldier, Levi Ackerman, and late member of the Special Operations Squad, Petra Ral.
This ship was born when the fans noticed how deeply crushed Levi was by the death of Petra. By the way he gazed at her dead body, to how he took her Wings of Freedom badge, to how he watched grief stricken as her body was thrown off the cart as food for the Titans, to how her father spoke of marriage to him with a devastated look on Levi's face. All of these factors prove that Levi had some type of affection for Petra. As well, Petra also seemed to care a great deal about Levi. When Eren Jaeger first transformed into a Titan unintentionally, Petra's first instinct was to make sure Levi was alright. In addition to that, after Petra was killed by the Female Titan, her father came up to Levi as they were returning from the expedition, and explained to him how Petra sent him a letter saying how she was going to devote herself to him. This proves that Petra also had great deal of affection for her captain.
The Ship Name
The RIV part is from Rivaille, the romanticized version of Levi. The ETRA is from Petra. It is sometimes also known as "Levetra" or simply "Rivetra."