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Well, the short answer is that the witnesses produce and validate the blocks for the blockchain. Every time someone posts, votes, transfers funds, etc. those transactions have to be processed and stored in the blockchain. That is the primary duty of the witnesses.

Witnesses also have other responsibilities as well, such as voting to approve or deny hardforks, telling the blockchain what the current price of STEEM is (so it can calculate rewards, and process SBD->STEEM conversions), and setting various blockchain parameters such as the cost to create new accounts.

Most witnesses also do other projects to improve the platform and community in various ways.