I think should be…
Like a bookmark link.
Click to bring the mouse text cursor (the “caret”) to the search bar (search field) which is at the navigation menu of the current page.
I see. Thank you.
The reason I like to have it, is to guide the visitor that there is actually a search bar which they can use to search for information within the website. Some may not realise or see the magnifying icon.
Thank you for your reply.