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Let me try to explain this to my best understanding. Like other decentralized cryptocurrencies, Steem needs a network of participants to validate the transactions, make them a part of the blockchain and allow all services built on steem to access the data. Since the currency is "mined" by participating in the network by producing and curating content, there needs to be another set of participants who would run the software that allows us all to use the network and to maintain the blockchain itself. Those users providing this service for the rest of us are called witnesses and they receive their own mining rewards for their work much like in other cryptocurrencies. There are 20 official witnesses that are determined by voting and needless to say, they play a very important role for the community. That's why it's important to select the best people for the job.