If your group is moderated, then you (or another moderator that you appoint) need to approve all messages. You can do this several ways.

From the My Groups page:

• The number of pending messages will appear under the Messages Pending column. If you have messages, the number will be linked. Click on this link, which will take you to the Pending Messages page.
• Review, edit, approve or delete the pending messages by clicking on the appropriate link.

From the Messages page:

• Click on the Pending section in the Messages area. You’ll see a list of pending messages (if any exist).
• Review, edit, approve, or delete the pending messages by clicking on the appropriate link.

From email:
If you’ve selected to receive notifications of pending messages (available in the Email Notification area of Edit Membership), you’ll be notified via email every time there’s a message awaiting your approval. You can either reply to the message or click on the link in the notification email.