A single search is designed to find Info Items that match the defined criteria (for instance, projects that were created on or before a certain date and/or have a particular attribute and/or containing certain keywords, etc.). But all of this criteria only define characteristics of items themselves (projects in the case). What if you want to find projects that have (or don't have) Tasks that are not completed or Appointments that are in the future? Nested Searches using the Relational criteria operators are the key.
Note: Available in Professional edition only.