W3C is an abbreviation of the World Wide Web Consortium and is the standard by which every single website is evaluated.
W3C errors highlight areas that can be fixed in order to improve the technical quality of a site. Even though is doesn’t really have an effect for SEO, it is still something taken into consideration as it can improve the websites usability and also the browser compatibility.
The W3C validation tool is considered as useful because it is able to process many different markup languages that all the different websites use and is not just limited to the main HTML language.
By having as little W3C errors on your site as possible, it becomes easier for a website to move to different platforms. This also has a positive effect for the search engine bots aswell as they will not have as many, if any, obstacles to move around in order to read the site.