The Mobile Messaging Inbox stores activists' replies to your mobile messages, if they meet certain criteria (explained here).
Go to the 'Start Organizing' menu and select 'Mobile Message Inbox'. Here, you'll see a list of all the activists' conversations, sorted in reverse chronological order, with the newest message at the top. You can page through the conversations, or search conversations by name, email address, or mobile number. You can also filter messages by unread or read messages by clicking the 'All Conversations' drop down menu. You can mark all messages as read by clicking the button below the search bar.
To view a conversation, click from the list on the left side. This will show the activist's reply to your message, as well as some of their core fields and subscription status. You can mark the conversation as unread by clicking the button below their name. You can reply to the messages, view the ladder or mass mobile messages they've received recently, and view the character count in the lower left. Refresh the page to see any new replies.