The Symbiont was a sentient vermiform lifeform from the planet Trill. It was transferred from one humanoid Trill host to another upon the death of the host. Humans could also be used as a host to a Symbiont, however the Symbiont could not remain in their bodies for long without physically harming the Human host. (TNG: "The Host") A Symbiont could survive in a partly Trill host normally. (DS9: "Children of Time") The Symbiont took with it all memories of the previous Trill hosts. Upon joining, the new Trill host gained these memories. The Symbionts lived in the Caves of Mak'ala on Trill and were cared for by the Guardians. They communicated with each other via electrical impulses transmitted through the milky water they inhabited.
The Symbiosis Commission oversaw the joining of Trills and Symbionts. The general belief in the 24th century was that one in every 1,000 Trills was suitable for joining; however, the number was nearer to 50% of the population. This was a closely guarded secret because every year about 5,000 Trills became initiates while only about 500 symbionts became available. (DS9: "Equilibrium")
Rites and ceremonies
The series bible of Star Trek: Deep Space Nine mentioned that "Many centuries ago, the symbionts lived underground while the humanoids were on the surface... and due to an environmental disaster, they were forced to 'join' to survive". 
For TNG: "The Host", the design of the symbiont was based upon a caterpillar with an octopus' head, but when next seen in DS9: "Invasive Procedures", the design had changed significantly, having what Michael Westmore refers to as a more "streamlined" design. (Michael Westmore's Aliens: Season Two, DS9 Season 2 DVD, Special Features)
The Trill symbionts show many similarities to the Goa'uld and their subspecies, the Tok'ra, from the series Stargate SG-1. Those species are technically parasitic, however, not symbiotic. The Trill symbionts also made their debut before the other series aired.