Hugo Kornelis digs into table spools:
The Table Spool operator is one of the four spool operators that SQL Server supports. It retains a copy of all data it reads in a worktable (in tempdb) and can then later return extra copies of these rows without having to call its child operators to produce them again. These copies can be made available in the same part of the execution plans, or in another part.
Table Spool is probably the most basic of the spool operators. The Index Spool operator is very similar to it, but indexes its data to allow it to return only a subset of the stored rows. The Row Count Spool operator is optimized for specific cases where the rows to be returned are empty. And the Window Spool operator is used to support the
RANGEspecifications of windowing functions.
Typical use cases of a Table Spool are: to reproduce the same input multiple times without having to re-execute its child nodes (e.g. in the inner input of a Nested Loops); to make the same input available in multiple branches of an execution plan (e.g. in wide update plans); or to ensure that an original copy of the data is available after an insert, update, or delete operator changes the base data (“Halloween protection”).
Click through for a great deal more detail.