If we explain it briefly:

Speed:   Fast websites gain an additional SEO benefit compared to websites that are not so fast. Actually speed is one of the SEO factors that is known  so there is no doubt that it can affect your rankings.

Security: Websites hosted on servers that are not well protected are vulnerable to attacks by spammers. This may not sound important but there are ‘spiders’ crawling the web looking for unsecure servers. Once they find one, they will hack into your website and run malicious scripts that will either redirect the users to a spammy website or add links to your pages pointing to other websites. It happened to me a lot of times and I can tell you is not a very good experience.

All hosts received from MailBox have antivirus service on the servers.

Uptime: Nobody (including Google) likes to go to a website and get a message that ‘site is not available’. There are hosting providers that they don’t take this very seriously but there are also hosting providers that strive to offer 100% uptime.

In terms of SEO if a website is constantly unavailable Google will decrease its ranking position since it does not offer a good experience for its users.

Support: Support is very important and it is indirectly related with SEO. Your hosting provider should be able to help you with a number of things related to website and server management that are sometimes related to SEO.

For example if you need to make your website SSL (that is https), the hosting provider should be able to guide you (or even do this for you). Choosing a provider that has good support can make a lot of difference when you are in need for help.