Normally the Twitter feed does display the images.
When an image is not public (for instance when it is marked as not appropriate for all audiences), it will not be shown in your feed.
Also, there is a difference between images that are uploaded via mobile phone and via pc. Those from pc are handled as a link to another website, so it will only display a link. The images from mobile phones are compressed and therefore able to be published directly on Twitter.
If you check your Twitter feed in Twitter.com, you'll probably see this different ways of images; some are only links, some will be automatically displayed.