Delegated Proof of Stake (DPOS) means the blockchain network is maintained by a small group of operators. Each operator is elected by votes from the members of the community and controls a part of the network according to his stake in it. Their main task is to be sure that no transaction is lost and that the blocks are produced according to the specs. Blocks are containing transactions (money transfers, blog posts or comments like this one). For the fact that they are maintaining the network, they are paid, also according to the stake they have in the network.

In other systems, like Bitcoin, the network integrity is maintained by Proof of Work, or mining. In exchange of this service, mining farm operators are paid directly in Bitcoin when they produce a block.

In Steemit, these operators are called witnesses and their main task is to produce a block every 3 seconds. Each minute, the first 19 witnesses are getting each a block to be produced, and one runner-up witness also gets the remaining block, by rotation. In the current implementation there is also a block allocated to the miners each minute, but that will change in future implementations.

Hope it makes more sense now. If you have questions, go ahead!