From the documentation:

Routing Address for Remaining Replies

When you configure RMM in your account, enter an email address to receive all the messages not identified by one of the reply rules. These messages forward to that routing address even if you send an automated response. Do not use an email address from the domain delegated to Marketing Cloud, as this action could cause unpredictable reply behavior.

The Routing Address is the “real” inbox where you want all the remaining replies to go, but you do not want to disclose it to your subscribers.

Eg. You want everyone to reply to a “fake” RMM email address [email protected], which will intake and filter all responses. The ones that were not filtered out by RMM and need taking care of will be routed to the routing address, which is a real, physical inbox, eg. [email protected]

For more details see here: https://help.salesforce.com/apex/HTViewHelpDoc?id=sf.mc_es_reply_mail_management.htm&language=en_US

From the documentation:

Routing Address for Remaining Replies

When you configure RMM in your account, enter an email address to receive all the messages not identified by one of the reply rules. These messages forward to that routing address even if you send an automated response. Do not use an email address from the domain delegated to Marketing Cloud, as this action could cause unpredictable reply behavior.

The Routing Address is the “real” inbox where you want all the remaining replies to go, but you do not want to disclose it to your subscribers.

Eg. You want everyone to reply to a “fake” RMM email address [email protected], which will intake and filter all responses. The ones that were not filtered out by RMM and need taking care of will be routed to the routing address, which is a real, physical inbox, eg. [email protected]

For more details see here: https://help.salesforce.com/apex/HTViewHelpDoc?id=sf.mc_es_reply_mail_management.htm&language=en_US