The biggest advantage of the shared web hosting is very cheap rate. The price of the single server distributed among different hosting accuont. You can enjoy shared hosting services with only $1 to 10$ permonth.
VPS or virtual private server hosting is the next level of hosting above shard hosting. When you have VPS hosting you will not have to worry about the security because you can customize it to the needs you have and make sure you have the right amount of security.
Dedicated web hosting offers you the resources and capabilities of an entire server. With a whole server completely devoted to you and your websites, you will always have enough bandwidth and memory to handle exponential amounts of traffic and any kind of data transfer.