VPS is a bunch of virtual macines running on a server. Each account gets a certian amount of processor and ram, they all run without connection to eachother. It looks like a dedicated server in pretty much every way. You do get root access to your instance.

How many accounts per server varies by a lot of factors. The better the hardware the more accounts it can hold, different plans provide different sizes and most cheaper hosts oversell quite a few times over.

VPS is a good way to get root access to a server without paying for all the hardware like you would a dedicated server. This is ideal for solutions that need custom software but don't use lots of resources.