Annihiliationism holds the speculative view that when a person dies, nothing continues to any sort of "other life". It stands in opposition to the position of eternalists, who hold that there is some sort of inner entity that continues after death. Both positions are at extreme opposite ends of a spectrum.
Often a Straw Man argument is lodged by eternalilsts against persons who do not hold either view, that claims that this "holding no view" is a form of annihiliationism, or that it is "eel wriggling". The Buddha's Noble teachings, the path of discernment, set aside any need for such speculative views to base a moral code upon, rendering such arguments, either way, irrelevant to his moral code, and to his noble teachings and practice. The Buddha himself professed neither view, and the eternalists' straw man arguments paint the Buddha Himself as an annihiliationist, or as an "eel-wriggler", both of which were in fact claims made by eternalists toward Him in his day.