The compatibility is a beta feature focused on third party search plugins that use Ajax / Autocomplete for displaying results as autocomplete. Usually free plugins do not search for custom taxonomies. If you are using a paid plugin probably you can keep the integration disabled.

Enable integration with ajax search plugins: Turn on to enable. If user type a brand name, it will be included in the autocomplete results #

Search form autocomplete: #

– Show brands and products from the searched brand: When customer type a brand name it will be shown the brands that matches with the keyword and also all products from the brand. Ex: if user types apple, it will show Apple and the Apple Products (limited to 10 entries)
– Show only brands list that matches with the search: It shows only the brands and not the products inside the brand
– No integration: Disable the feature

If your plugin is not supported you can open a support ticket and we check if possible to integrate on future releases

Current supported plugins:
– Advanced Woo Search – Free
– YITH Ajax Search – Free