Delegated Proof of Stake, DPoS for short, is a very innovative consensus algorithm. You could say that it is a kind of democratic PoS system. It was created as an alternative to the "old" Proof of Work system, which as we know requires a lot of work to make it work. PoS and DPoS, in contrast, do not require as many resources and it is a more economical consensus.
Such a mechanism was designed as a project to eliminate the problems associated with Proof of Work. This ranges from general network security through the costs associated with network maintenance and so-called cryptocurrency mining including expensive hardware. In a typical PoS there are no miners and nobody mine anything. Validation of subsequent blocks depends on the number of cryptocurrencies held by nodes. The more nodes a node has, the higher the chance that it will be the validator of the next block. This is another advantage of PoS over PoW. It is not the power and investment that is in the hands of the node but the internal system, its own cryptocurrency. This is known as internal investment by the way.
And what is even better. The PoS system makes a 51% attack virtually impossible for a simple reason. You need to have more than 51% of all tokens to launch a successful attack. And when you launch an unsuccessful attack the financial loss to the attacker is high. DPoS on the other hand is something similar to PoS but still new.
Daniel Larimer is the creator of this DPoS. You may know him from Steem, Lisk or Bitshares. Hive is currently using DPoS and is doing quite well. Networks like DPoS use a voting system where token holders delegate the maintenance of the blockchain network to third parties. These are called delegates and our votes are to secure the network along with their work. They are the ones who vote and approve new blocks. Along with each block, the so-called witness or delegate receives a block reward. The biggest plus that DPoS networks bring is gigantic scaling and for example for Hive also free transactions.
To conclude, DPoS is derived from PoS and it in turn is derived from PoW. This democratic selection of delegates that we think are best for the network is a very cheap solution compared to PoW. More transactions per second and a different way of creating blocks is also a great advantage.