(covers information from several alternate timelines)
The soul was often described as the spiritual essence of an individual. Many cultures had a concept of a soul, but there were different interpretations. Many religions on Earth had a concept of a soul.
When Captain Gabriel Lorca confessed to having killed the crew of his previous command, the USS Buran, to prevent them from having to endure Klingon torture, Harcourt Fenton Mudd commented that confession was good for the soul, but it was too bad none of them had one anymore. (DIS: "Choose Your Pain")
In ruling on the question of whether Commander Data was the property of Starfleet, Captain Phillipa Louvois stated that she did not know whether Data had a soul or even if she had, but ruled that he had the freedom to explore the question himself. (TNG: "The Measure Of A Man")
In describing the panic accompanying the prophesied return of Ardra on Ventax II, Doctor Howard Clark explained that the people there believed that they had sold their souls to the devil. Later, when an impostor posing as Ardra proposed terms for arbitration regarding her claim to the planet with Captain Jean-Luc Picard, she demanded a steep price of him if he lost; she wanted "your heart, your mind, your soul, and I want you to give them to me without resistance, of your own free will." Later, in describing his dilemma to Lieutenant commander Geordi La Forge, Picard told him "my reputation as a litigator, not to mention my immortal soul, is in serious jeopardy." (TNG: "Devil's Due")
Bareil Antos felt that "When you overindulge the body, you starve the soul." When Antos's mirror universe counterpart visited Deep Space 9, Major Kira Nerys took a great interest in him, having been the lover of the Bareil Antos from the prime universe. Unfortunately, the mirror Antos had been sent there to steal an Orb for the the Intendant. When Kira tried to stop him from doing this, the Intendant (Nerys's own mirror universe counterpart) commented, "Isn't that sweet? She is still trying to save your soul. Of course, you don't have one." (DS9: "Resurrection")
The members of Chakotay's tribe believed in the soul. The medicine wheel could be used to guide the soul based on the placement of the Coyote Stone. Placing this stone between the crossroads of the Fifth and Sixth Realms was believed to divert the soul into the Mountains of the Antelope Women. (VOY: "Cathexis")