Shared hosting is, when multiple websites are hosted on the same server or on the same IP address. The alternative is when a server or an IP address is dedicated to a single website which is, dedicated hosting. These are usually common set ups.
Using shared hosting is perfectly fine and does not negatively affect your site in Google Search. Sometimes, when too many websites are hosted on a system with limited capacity, it can happen that the server is overloaded. This can result in the server and its websites becoming very slow. The same thing can happen with a dedicated hosting, though.
Having a website hosted on a slow server makes your users unhappy and can make it harder to crawl. Just to be clear, a dedicated server is not always fast, and a shared server is not automatically slow.
Another concern we sometimes hear is that there might be other bad websites hosted on the same server. In SEO, this is called “server in a bad neighborhood”. This is not something to be worried about.
For Google, this is fine and not problematic. Google will treat each website based on its own merits, not based on its virtual neighbours. So in short, for Google, using shared hosting is perfectly acceptable. There is no need to move to dedicated hosting or a dedicated IP address for SEO reasons.