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Witnesses are the people who actually run the steemit block-chain (the auditable history of truth, the wallet system etc.). Witnesses earn money from this but they must have powerful equipment that is online 24/7/365. Its important to vote for witnesses that you feel you can trust, as in theory they could try and tamper with the site, though that is quite hard to do in reality.

The witnesses I have voted for are sc-steemit and moisesmcardona, because I know them from the Gridcoin community and they have shown to be reliable there.