Saving a search will capture the search parameters so that you may replicate a search in the future
Clicking on “Save search” will save all of the parameters of your search to replicate this search in the future. 
Because we have a variety of search parameters to choose from (you can add a bunch of terms, remove terms, change the map position, and add combinations of filters), this feature allows you to save a collection of well-crafted search parameters and come back to it at another time. If you are looking at the lease agreements for a shopping center and inputting all the terms they have exclusives with, you can save the terms without having to enter them again the next time you do a search for a particular use case. This is a great feature for users who have multiple centers as you can use the same search in multiple markets.