PostgreSQL + query planner + amount of entities
You may have missed that spot in the chapter of the manual you quote:


  Note also that since ANALYZE uses random sampling while producing
  statistics, the results will change slightly after any new ANALYZE.


Emphasis mine.

If you actually mean "how many" rows in your question: the query planner has selectivity estimators for certain operators in the conditions. In combination with the statistics gathered the planner estimates the number of rows for every step.

Details of row estimation can be found the chapter of the manual you already link to in your question.

Estimations can be way off if the data distribution is very uneven within a table. That's why raising the setting for default_statistics_target (and running ANALYZE afterwards) may help in such cases.

Some special operators have special selectivity estimators. Like text search. Details in the source code in src/backend/tsearch/ts_selfuncs.c