The memo key is used for encrypted memos attached to a transfer of funds from one account to another. Memos can be encrypted by the memo private keys. The encrypted memo can only be read by the receiver, so it can serve as a private messaging system with each message will cost a minimum of 0.001 STEEM/SBD.
A user can find their public memo key by going to https://steemd.com/@your_username under the "Authority" widget. Alternatively, he/she can find their private and public memo key by going to https://steemit.com/@your_username/permissions.