When a visitor submits a search request from your website in a translated page, Linguise will first translate the search request.
For example, the visitor search for Bonjour in a French page, then Linguise will translate Bonjour to Hello and then will make the request to the original website.
The request to the original website is like if your visitor was searching for Hello on your website without translation. Then the search request is returned in the translated language, here it would be French.
Note that the search feature is implemented wor WordPress native search, Joomla and WooCommerce.