Felicium was the vaccine for a plague that existed on Brekka's neighboring planet, Ornara sometime in the 22nd century. It was made by a complex and expensive process, including the harvesting and cultivation of the originating plant, and its distillation into the final product.
The euphoria experienced when taking felicium was immediate and seemed to be somewhat sedative and pain relieving, similar to planet Earth's opiates. After taking the drug, the individual would eventually experience withdrawal symptoms within 72 hours.
The vaccine was supplied by the Brekkians in exchange for goods. Even after the plague was over, the Ornarans had unknowingly become addicted to the vaccine, the terrible withdrawal symptoms leading them to think they were still affected by the disease, and Brekka continued to produce it for them in a profitable business. It became the Brekkians' only product. As years passed, the Brekkians refined the drug to make it more and more potent. (TNG: "Symbiosis")