You can verify your videos are claimed by you by logging into your channel and clicking the top right pull-down menu and then clicking Video Manager.
This icon means that your video has not been monetized. Click on the icon to set your monetization settings.
This icon means that your video is monetized and earning revenue!
This icon means that YouTube needs more information in order to monetize your video. Click on the icon to start the process.
This icon usually means that your video is under review for monetization. Hovering over the icon will give you more information.
This icon means that your video has been removed, or rejected for monetization. YouTube should have sent you an email with more information.
To learn more about video monetization and the ads you can enable, check out this article.