Tail risk conventionally refers to the risk of a large and sharp draw down of the portfolio. How large is subjective and depends on how you define what is a tail.
A lot of research is directed towards having a good estimate of the tail risk. Some fairly new research also now indicates that investors perceive tail risk to be a stand-alone risk to be compensated for, rather than bundled together with the usual variability of the portfolio. So this risk now gets even more attention.