When this property is set, it tells the search engine that it needs at least this many total hits that match the query... but not in the result set... only as a total of the number of hits. This comes in handy in custom paging implementations. For instance, if you show three page options at the bottom of the page (ie: you're on page 3, so you show pages 4, 5 & 6 as options) and you set your paged result set to 25, then you likely want to set this value to 3*25=75. 75 is now an estimate, but it is guarenteed that your query will return at least 75 hits.
This property is commonly used in conjunction with the ResultTable.TotalRows property.
Note that higher values of TotalRowsExactMinimum will have a negative perf impact.