A Hash Table is a data structure used to store data in the form of Key=>Value pairs. A Distributed Hash Table (DHT) is basically a hash table distributed across a network of computers(nodes). A DHT uses a Routing Protocol to determine which node to store a piece of data on.
A distributed hash table (DHT) is a class of a decentralized distributed system that provides a lookup service similar to a hash table; (key, value) pairs are stored in a DHT, and any participating node can efficiently retrieve the value associated with a given key. Responsibility for maintaining the mapping from keys to values is distributed among the nodes, in such a way that a change in the set of participants causes a minimal amount of disruption. This allows a DHT to scale to extremely large numbers of nodes and to handle continual node arrivals, departures, and failures.
A DHT uses a Routing Protocol to determine which node(s) a data should be stored on. This routing protocol usually takes care of replicating data and also updating data stores to make sure that the data survives on the DHT for the long term. Some popular routing protocols are Kademlia, Chord and Pastry