A soul (魂 Tamashī) is understood, in the Saint Seiya mythos, as the vital part of a living being, and what allows both mortals and deities to reincarnate through the ages. Souls have originally been seen in the Yomotsu Hirasaka hills on their way to the underworld, but there have been other appearances.
The immortal soul of both mortal and gods is made up by the cosmoenergy originated in the Big Bang, called the "Big Will". In the original series, the concept of a soul was promptly revealed but little explored, as the author decided to focus on the ways people can use and bend the cosmo itself. When Dragon Shiryū went to Jamir in search of an alchemist who could revive the Pegasus and Dragon bronze cloths, he met skeletons in the way. The skeletons were former saints (who even wore deceased cloths), and all attempted to kill the Dragon so that he'd join them, who had all failed in the same task. These skeletons retained their souls due to the local curse, and were all doomed to haunt the narrow misty passage to Mū's pagoda. After being defeated by Shiryū, the fate of their souls is unknown.
Dragon Shiryu met souls once again in his fight against Cancer Deathmask. In the Cancer Temple, the ripped off faces of Deathmask's victims were bound to the house in the form of ghosts. In a similar manner, the souls of ghosts gathered at the temple during the 18th Century, but its guardian saint, Cancer Deathtoll, dedicated his time to send the dead peacefully to the underworld with his special coffins, rather than imprisoning them. The souls of mortals such as saints are at times passed down to a later generation, as are those of most (if not all) gods. Specters are a special case, as the 108 stars are both immortal and bound to Hades, and will return at each generation to fight by his side. The only thing that makes a specter die is the sealing of the soul, which is similar to that of deities.
Main article: Saint Seiya: Episode G
Main article: Saint Seiya Omega