Let $a_1, \; a_2, \; a_3, \; \dots$ be a sequence, which I'll call $S.$ Then a tail of $S$ is any sequence of the form $a_n, \; a_{n+1}, \; a_{n+2}, \; \dots$ where $n$ is a positive integer. Thus, a tail of a $S$ is simply all the terms of the $S$, in the same order, except that at most finitely many initial terms of $S$ are omitted. Note that one of the tails of $S$ is $S$ itself, and every tail of $S$ is a subsequence (of a certain special type) of $S$.