Filters are a way to narrow down search results by only displaying issues with specific attributes.
After executing a search query, YouTrack displays the Filters area to the left of the list of found issues where it shows different attributes and values that these attributes have within the set of found issues.
For example, here's how issues within the current set of found issues are distributed by creation date:
Of all issues in the set, 28 issues were created today, 6 issues yesterday, 253 last week etc. By default, the All check box is selected, which means that the whole set of found issues is displayed, irrelevant of when they were created.
If you only want to view issues that were created today or yesterday, select Today and Yesterday. YouTrack will shrink the set of issues to only 34 issues (28 created today and 6 yesterday), and the corresponding query will appear in the search box.
You can further narrow down the list of issues by using filters for other attributes (State, Tags, Subsystem, Assignee etc).
Note that the query in YouTrack search box is automatically synchronized with filters as you modify them.