Search Engine Optimization (SEO) is mostly a function of following the current Webmaster Guidelines from the major search engines. However, your webserver performance can have an impact on how your website ranks. The search engines have stated that they are trying to rank the 'best' websites for any given keyword query. This includes both on site and off site issues.
Here's some areas where your web hosting company can make a difference;
Uptime
If a search bot tries to crawl your site while the network is down it will certainly affect your rankings.The algorithms may flag the website as unreliable.
We have 100% network uptime. That means that within the data center, the website is always live and available to resolve worldwide. Our cloud / grid technology has no single points of failure. (of course, all kinds of things could happen between the date center and the end user)
Server Response Times
The search engines are now ranking sites for their 'Page Load Speed'. This can occur when a web server is hosting hundreds of websites and a couple of the sites are using huge bandwidth. Other sites on the server will load slowly. One of the major hosting companies states in their terms of service "....Web Sites may experience periodic decreases in performance."
Our servers are load balances, with multiple instances of your website resolving across dozens of servers. While individual sites can exceed their bandwidth limits, the remaining sites have guaranteed (hard coded) bandwidth available at all times.
Your IP Neighborhood
All search engines segregate certain topics, These includes gambling, adult and pharmaceutical sites. If an IP address becomes populated with these topics then everything on that IP address may find their rankings diluted.
Our terms of service state that we only host business websites. Nothing controversial, nothing to raise any flags.
OS Updates and Plug Ins
Keeping the various software components on a web server up to date is important mostly due to potential malware and hacking issues. Once a cite is tagged as having malware your rankings will drop dramatically. The 'reinclusion' process, once the website is cleaned up can take weeks.
Our servers are always updated to the latest 'stable' release of Apache and CentOS.