The "Cloud" basically reffers to more than one computer, or server if you will, being utilized to provide services for one or more processes. Using this technology for hosting both has its advantages and disadvantages over shared and dedicated solutions.
The cost of cloud computing, though a more efficient technology in most cases, tends to vary greatly as do the services provided. The idea is "why pay for what your not using, its a small planet lets be efficient". While this may sound hunky-dory, lets dive in a little deeper..
Cloud hosting is a lot like shared hosting in that you'll be sharing resources with others, the major difference is that those services are split amongst many computers. This make things like server lad easier to manage because your processes can be sent to another machine with free resources. Data is treated the same in that your files can be scattered throughout many different hard drives. It makes scalability more efficient and less costly, at least in theory. Sounds great right?
Diversity can be a great thing when dealing with things like stocks and investments but data is not like dollars. Scattering your data around just doesn't feel very secure to me. If my data is spread across many computers then the risk is increased when facing hardware failures and again, like shared hosting, it tends to be a bit more dificult to maintain security when your files are laying next to someone elses.
On the flip side, "dedicated cloud" hosting is a totally different story, here you are basically using your cloud of computers as one - if you are in control of all of them then this really can't be beat. You will however have a long way to go before you need a solution like this if you are just getting started so unless you have terabytes and terabytes of data that needs to be managed, I wouldn't worry about it for web hosting.