A Saved Search is a search you can decide to receive notifications about. Every time a new property that matching your criteria is listed, you will receive an email notification. This way you can reply quicker to new listings and potentially be selected as a tenant.
In your 'Settings' you can adjust the frequency of notifications.
A few extra tips to get the most out of the Saved Search
If you save a search to stay up to date for a certain city, you can also choose to make your public profile visible for landlords and roommates in that city. If your profile is visible for landlords and roommates, they can approach you in the tenant search.
Make sure to specify what kind of property you are looking to receive notifications about. You do that by filling out all filters. Also make sure to complete your profile and upload photos to give landlords you've contacted the full picture about who you are and what you do.