The search function on the catalog page searches for keywords in the video or collection Title, Full Description, and Tags. Results will only be returned if the searched word is included in one of these three fields.
When creating or editing video or collection settings, ensure the desired keywords are included in the Title or Description.
Tags are found under the SEO tab.
Your customers can also search by the custom filters you've added. You'll find Category and Author are two of the default filters, but as you create any custom filters they will be usable by your end-users too.
Just note that filters are single select, so when you click say the Category filter you can only select one category at a time to filter by. Once your customers have filtered, they would need to remove any applied filters(or simply reload the catalog page) to go back to non-filtered view.