A probiotic - "A preparation of or a product containing viable, defined microorganisms in sufficient numbers, which alter the microflora (by implantation or colonization) in a compartment of the host and by that exert beneficial health effects in this host."
The term prebiotic was introduced by Gibson and Roberfroid (42) who exchanged "pro" for "pre," which means "before" or "for." They defined prebiotics as "a non-digestible food ingredient that beneficially affects the host by selectively stimulating the growth and/or activity of one or a limited number of bacteria in the colon." This definition more or less overlaps with the definition of dietary fiber, with the exception of its selectivity for certain species.
The term synbiotic is used when a product contains both probiotics and prebiotics.
Source: Schrezenmeir, Jürgen., de Vrese, Michael. Probiotics, prebiotics, and synbiotics—approaching a definition. American Journal of Clinical Nutrition, Vol. 73, No. 2, 361S-364s, February 2001