This is one of a pair of query hints that can manage the memory grants of individual queries. The maximum memory grant hint allows you to limit the amount of memory an individual query can use. If the hint specifies a value lower than the amount of memory required to execute the query, the query will request the required amount. This is like a granular resource governor. For the rest of this post I will concentrate on the minimum memory grant query hint.
When the query optimiser builds an execution plan for a query, it calculates how much memory is required for the query to execute. This calculation is based on the estimated number of rows (used in sort or hash joins) and the average size of these rows. The optimiser calculates the least amount of memory required to perform the operation (required memory) and the amount of memory required to perform the whole operation in memory (desired memory). Each time the query is executed it requests a memory grant from the server. The query will perform much better if it’s granted its desired memory or more. If at run time the query has to perform sorts or hash operations on more than the estimated number of rows, it will spill to tempdb. Spilling to tempdb can be orders of magnitude worse for performance as your data has to be written to disk causing more IO.
This feels like the type of thing you might want to do once for a particularly recalcitrant query, but not something you want to do regularly.