By default, WooCommerce provides a very simple search solution, without live product search or even SKU search. FiboSearch (Ajax Search for WooCommerce) provides advanced search with live suggestions. It is one of the most popular WooCommerce product search plugin. It gives your users a well-designed advanced AJAX search bar with live search suggestions.

Some of the features are
Search by product title, long and short description
Search by SKU
Show product image in live search results
Show product price in live search results
Show product description in live search results
Mobile first – special mobile search mode for better UX
Easy implementation in your theme – embed the plugin using a shortcode, as a menu item or as a widget
Terms search – search for product categories and tags
Limit displayed suggestions – the number is customizable
The minimum number of characters required to display suggestions – the number is customizable
Personalization of search bar and autocomplete suggestions – labels, colors, preloader, image and more