Here's the deal. Google keeps track of IPs of sites in its engine. Sites with the same IP are typically on the same server. If this is a shared server, the sites might not have a lot in common other than using the same hosting company. But if this is a dedicated server, especially if the sites link to each other, Google assumes they are run by the same person and part of the same network. Therefore, a backlink doesn't count as much as it ordinarily might - it counts more like a backlink from one page of the same site to another.
The problem is that the search engines don't know whether an IP is to a shared or dedicated server. This can be a problem when another site that might be hosted on the same IP as you does some black hat SEO or something to get it banned. It's very possible that your site might also inadvertently get banned.
Hence why it's a good thing to have your own IP
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