There are number of factors that associate with web hosting servers having direct impact on SEO for your website.
Just take an example you are transferring the hosting of your website to other host providers, and the settings are not yet updated by new host providers which results in your web page to not get displayed. This may further results in higher bounce rate, no traffic and more , and impact your position in search engines.
Webhosting effects come under on page SEO and it strikes the on-page seo of your website for many reasons. Standing in year 2016 and having a poor web hosting can really drop your achieved ranking.
A poor load time can be one of the important factor when the world moving faster this world, no one can wait to open your website in minutes.
An IP also plays a a good role while practicing for for Geo based seo.
A good host may not boost your ranking but a bad host can get your site blacklisted in the search engine. A bad host is usually cheap host that is insecure and easily attacked by hackers. Since you are on a shared hosting plan, you are sharing the same IP with thousands of other websites on the server. If someone create a lot of spam sites and host them on the server and they get blacklisted, your website will also be blacklisted.
There are no effect of web hosting server if you are choosing a good web hosting server. But if you are choosing free web hosting server it's effect in search engine optimization. Because they some time down your server or your website not open all time.