Question
What is long-tail latency or tail latency?
Answer
Tail latency is the worst performing time-measured response from an application. Outliers can be described as requests that take far longer than others in a statistical sample. Such irregular durations, with long latencies, are said to be at the tail-end of a chart or graph. Long-tail latency would generally refer to the worst 1% or worst 2% of the requests. (One source of this article is this external posting.)
See also page 15 of Designing Data-Intensive Applications by Kleppman. You may want to read about SLIs and SLOs here.