Site search
The search in the header searches the site's pages and its items (and item sets, if the site is set up for it). Results come grouped by kind, with item cards, and a button to see all results of a kind.
Choose what the site search covers (site pages, items, item sets) under Site admin › Settings, in the Search section.
Advanced search
Item and item set browse pages link to the advanced search: by property values, class, template, item set, media and more. The form uses the theme's fields and buttons.
Search across all sites
If your installation has several sites, Omeka can search all of them at once: under Site admin › Settings › Search, set Search type to All sites. The header search then looks across every site, and results show which sites each item belongs to. A result opens in the current site when it is part of it, and otherwise in the first site it belongs to.
Search box blocks
BlockSuite's Search box block puts a search field anywhere on a page, for example on the home page.