Ok shared account you are limited in what you can do eg you might not get shell access and you wont get root access, This means you can not install extra services or some things things like extra mpeg encoders for video related servers. You also can be effected if another user on the server starting having CPU/memory/bandwidth spikes and your host is not keeping a close eye on the system.

A vps is a poor mans dedicated server, as said it is the next step up from a reseller/shared account but you have to remember that this is a virtual server hosted on a dedicated server. The memory and cpu will be monitored and you will have a set amount some times as little as 128mb so dont expect to run any thing too memory intensive. But the plus side is that you can reboot the virtual server or install any thing you want you have full root access and can pretty much do any thing you want with in your limits of your memory and cpu useage.

This is a good option if you want to start as playing a host or want to run a application that you have to install custom addons that would not be allowed if you ran a shared host.

Next step up is the dedicated server you are master of your domain you can reboot or install as much or as little as you want. You have full use of the cpu and memory, its a bit like having your own PC sitting in side a data center. You can use this for memory intensive application or if you want to run some thing that you might not want a host seeing. The server is yours to do what you please with. You could set it up a mailsystem a dedicated ftp server a torrent server you name it. You can do what you want with it as its your box.

CPUGEEK what would you want to run and members can advise or check out webhostingtalk as people will be falling over them selves to host you either as shared/vps or dedicated account.