To keep the explanation simple, I'll use Server 1 and Server 2.
Server 1 has 1 assigned IP address. When users sign up for the cheap hosting packages, let's say they're all assigned to Server 1. So you could literally have 20 accounts or more on Server 1 and each account could be hosting 20 sites or more. Sounds easy for all and is definitely cheap for the HostingCompany.
Here's the bad part. Look at IP addresses like neighborhoods. HostingCompany is given several blocks of IPs and assigns them accordingly to their servers. Lets say everyone with an account on Server 1 are hosting sites that share files, promote illegal content, adult content, or other 'bad content'. Then you come along, sign up, and get moved to Server 1. Google knows which sites are on what IP addresses. If it sees your site in a 'bad neighborhood' Google may be reluctant to rank you favorably. Although they won't admit that, you can research it and find many people have done experiments to see if this is true and most people will tell you it is. We've done our own experimenting and are very careful about how we allocate the IPs assigned to us and make sure they're 'clean' prior to use.
If Server 1 has a site on it that promotes blue widgets and you put a site on there that promotes the same, Google may 'flag' both sites since they may assume that both blue widget sites belong to the same owner. Google says the same person can't possibly promote the same items on more than one domain while making each site a good experience for the visitor.
Lets bring in Server 2. Each account that signs up and wants a dedicated IP will be pushed to Server 2 and have their own IP. So now if Server 2 has 20 users on there, each user has their own IP so Google and other search engines see this as 20 different neighborhoods. So if you put 20 sites in your neighborhood, all promoting different products, none of the sites link between each other, you should be alright. You've created a clean neighborhood.
That's the long explanation that includes some SEO in there for you. 🙂
BTW, the 20 users with 20 sites that I used are only examples. Servers can handle much more than that depending on their hardware.