Qatai was a pilot of a run-down ship who was obsessed with killing a ship-devouring protoplasmic beast, which lured in ships to consume by generating telepathic illusions to make them believe the creature was whatever the crew most wanted to see.
Qatai had been hunting the beast for thirty-nine years since it consumed a ship carrying his family, and had become mostly immune to the beast's telepathy, though he could not capture or destroy it. He had been swallowed by the creature when his latest attempt to kill it resulted in it tricking him with one of its illusions. When the USS Voyager began to approach the creature, he was able to transmit a weak message to warn them away, but the crew of Voyager, believing that they were entering a wormhole that would take them home, ignored his warnings as random fluctuations.
After Voyager was swallowed by the beast, Qatai beamed over to Voyager. Only Seven of Nine and Naomi Wildman were conscious, as neither of them had been especially bothered about getting back to Earth (The Doctor was also available, but he had been deactivated prior to entering the "wormhole", and, as an artificial lifeform, was immune anyway). Qatai explained the situation to them, and the four were able to come up with a means of tricking the beast into expelling them by making Voyager indigestible.
After Voyager had left, Qatai retired to make repairs on his ship before resuming his quest, asking his new friends to get their crew home shortly before he vanished from their lives.
Although he came across as a simple hunter, Qatai apparently had some degree of technical skill, saying that he once attempted to help someone subjected to the creature's influence throw off the illusion using a method similar to an attempt to lower the subject's neurotransmitter signals with a cortical inhibitor, only to be met with failure. While focused on his self-imposed mission to destroy the creature, he was not without compassion, treating Naomi Wildman with simple affection and expressing amusement at her description of the creature as a "pitcher plant" based on her biology classes, as well as exchanging jocular comments with The Doctor.