Please install both the Ignite Gallery search plugin, and the Ignite Gallery image inserter plugin. (In version 3.7 you just need to install the search plugin). The search plugin will display the search results, and the image inserter plugin will put images into the search results.
Enable the Joomla search module. Alternatively, you can go into the gallery profile settings, and in the general tab, choose yes for show search.
The search plugin will search the image filename, image description, image alt text, and image tags. It will also search the category name and category description.