Shared hosting is one in which a single physical server hosts hundreds or maybe thousands of websites. It is cheapest amongst all the three hosting option and most ideal for websites with low traffic.
Virtual private server hosting (VPS) is a newer form of hosting that seeks to combine important features of dedicated hosting like better control and security at the cost not too way above shared hosting.
Dedicated hosting is the most advanced form of hosting where an entire server and resources are at the command of a single website or organization. It is most ideal hosting option for traffic-intensive websites which receive the huge amount of hits on daily basis.