Trill symbionts were a sentient lifeform native to the planet Trill. They were able to live inside humanoid Trills where they formed a link and experienced what the humanoid Trill experienced. They had a much longer lifespan than their hosts and upon the passing of a host they could be implanted into another host and with them they took the previous host's memories, sharing them with the new host. This made them highly sought after and for a long time a closely guarded secret by the Trill.
The Symbiosis Commission is the body that controls the distribution of symbionts to the general population. It was believed that only a small percentage of the population was suitable for joining, however this figure was closer to 50%. This secret was kept due to the much lower availability of symbionts, some 300 a year, compared to those willing to be joined, 5000 a year. (DS9: "Equilibrium")
The symbionts could be joined with other humanoid species as well. It was possible for a Human to play host but could only do so for a short period of time before the joining caused physical harm to the host. (TNG: "The Host")