From my reading, publishing anything in AEM means it's ready for use and will appear in creation process. I have lot's of question about it like who can publish, why can I use my image assets even tho I didn't publish it. Who can add asset and administrator can Approve the Added asset. Need more explanation on each default groups that were created and it's permissions. But my main question for now is what is this and how can I approve this?
Answering my other questions are also appreciated. Thanks!
Navigate to the inbox and approve/reject the tasks associated to the workflows, that should get rid of pending status on content/assets. You could do it as an administrator or the user to whom the task is assigned.
Your Inbox (use 6.3 or 6.4 documentation per your AEM version)
Any user who has been granted appropriate replication ACL can publish the content (pages/assets/CF etc.) You are able to use the assets because you are working on the author instance where assets are present irrespective of their replication status. Replication would just push the content/asset from author instance to publish instance (separate AEM instance).