The main use of filters is for searching. An OBO-Edit search checks every term or link in the ontology to see if it matches the given filter. When the search is complete, a list of matching terms is displayed to the user.
The OBO-Edit term search panel looks like this:

To do a search, first use the filter designer to create the filter you want to use. Then click the "Search" button.
When the search is complete, a list of results will appear and a new tab will be added to the search interface. Term search results consist of a list of terms that match your search query. Each term's ID and name are listed:

The search results appear at the top of the tab. To sort the search results by a particular field (e.g., ID), click the appropriate header at the top of the search column. Clicking again will reverse-sort by the same column.
Click a search result to select it. The search result will automatically be selected in any panel set to global selection mode.
Each search result panel behaves as a component and can be handled separately; by default, new search results panels appear docked behind the search panel.
Note that you can control whether or not OBO-Edit includes obsolete terms in search results. The default is to include them. You can exclude obsolete terms from search results (including dropdown autocomplete lists) by checking the checkbox for the option "Exclude obsolete terms from search results" in the Configuration Manager. If you change the setting of this option, you will need to quit and restart OBO-Edit to see the change in search behavior.
You can do a link search by choosing "Link Search Panel" from the "Search" menu. Link search results consist of a list of matching links. For each link, the child name, child ID, type ID, parent name, and parent ID are listed:

As with term search results, link search results appear in tabs that behave as components, and the results can be sorted by clicking the headers. Clicking on a link in the list selects it in other relevant panels if you're in global selection mode; note that because each result is a link, no selection will appear in the Text Editor.
To control what information appears at the top of each search result panel, click the wrench icon. A configuration panel appears:

Check the first box to show the words "Search results:" at the top. Use the pulldown to select whether to show the number of matches ("Result Count"), the search parameters ("Query Expression") or no additional text.
You can save just the ontology terms that matched a particular search. The way to do this is with a filtered save.