Active keys are used to make transfers and place orders on the internal market of the Steem blockchain. Everytime a user does a transfer, he/she is signing each transaction with their active private key. Then, the system validates the transactions by using the active public key. Authenticated transactions are added to the blockchain, while non-authenticated ones are rejected.
A user can find their public active key by going to https://steemd.com/@your_username under the "Authority" widget. Alternatively, he/she can find their private and public active keys by going to https://steemit.com/@your_username/permissions. Finally, a user can change them by changing the password of their owner's key