The posting key is used for posting and voting on the Steem blockchain. Everytime a user post and vote through their account, he/she is signing each transaction with their posting private keys. Then, the system validates the transactions by using the posting public key. Authenticated transactions are added to the blockchain, while non-authenticated ones are rejected.
A user can find their public posting key by going to https://steemd.com/@your_username under the "Authority" widget. Alternatively, he/she can find their private and public posting key by going to https://steemit.com/@your_username/permissions.
Finally, a user can change their public and private posting key by changing the password of their owner's key