is a great post and I quote from it liberally below.

When you make a post WordPress allows you to define one of 9 post formats. This meta-data instructs the theme how to render your data. Unfortunately if you change your theme as is the norm for brochure and personal sites then this can break your posts.

For example, if you’re posting a video, there’s a video post format which can be used to put the video front and center and show it off in a different way than if it were just contained within the post content itself. There are 9 different post formats supported by WordPress (aside, gallery, link, image, quote, status, video, audio, chat).

Changing theme breaks the presentation because all of the post format metadata that they had entered over time will no longer be used and their posts will look nothing like their former selves. This is because theme authors never had a standardised way of adding post format metadata to their posts (like the featured video’s URL, or the main link that you’re talking about), so everyone came up with their own. As such, when you change themes, the post format data won’t match up with the new theme, so the new theme doesn’t know how to display your post format any more.