The Row Count Spool operator is one of the four spool operators that SQL Server supports. It counts the number of rows in its input data, and can then later return that same amount of rows, without having to call its child operators to produce the input again.
The Row Count Spool can be viewed as similar to Table Spool, but optimized for cases where the amount of rows is relevant but their content is not. Because the content of the rows is not relevant, the operator does not need to use tempdb to store its input in a worktable; it only has to keep a running count as it reads the input. The other two spool operators have different use cases: Index Spool is used to enable the spool operator to return specific subsets of the input multiple times, and the Window Spool operator is used to support the ROWS and RANGE specifications of windowing functions.
Read on to see where this might be useful and when it may appear.