Francisco looks at index spools:
When we are analyzing execution plans, we may come across different types of Spool operators – Table Spools, Row Count Spools, Window Spools or Index Spools – that the Query Optimizer chooses for specific purposes. In this post we are going to briefly look into the Index Spool, how it can sometimes lead to suboptimal query performance, and what can be done to easily fix it.
My favorite description of this is Erik Darling’s: spools are SQL Server’s passive-aggressive way of telling you “I’m not saying you need an index but you need an index.”