What is Page Life Expectancy precisely? What is the value returned by Page Life Expectancy, precisely? 

The use of the word "will" in this documentation


  Indicates the number of seconds a page will stay in the buffer pool without references.


suggests that the PLE value is a prediction of some kind. Is the prediction based on the actual computed average of the length of time pages now in the buffer pool have been in the buffer pool?

Is the algorithm used for computing PLE available?
PLE is a measure of how long (in seconds), pages are staying in memory.  It is more a measure of the age of the current pages, than a prediction.  But if the current load stays the same you should expect the PLE to stay the same.  

In reality, it changes, the value grows every second, until there is a big flush then it shrinks.

Related:


Page Life Expectancy (PLE), where to start?
SQL Prove memory pressure - high Buffer Cache Hit Ratio, but low Page Life Expectancy
How can you have a Buffer cache hit ratio of 100% with PLE of 103?