oEmbed refers to an API used by WordPress and many WordPress Themes like Layers to quickly embed content such as Tweets, audio or video players. In WordPress, share urls pasted into your post content to something like a YouTube video automatically pull in the video where the URL is placed. In Layers, the Video Embed field in the Layers Options on your Post Editor allows this embedded video or audio player to replace the post’s Featured Image, which is useful for placement of the content, as well as compatibility with the Layers Posts widget, for example. We strongly recommend using the Video Link field to take advantage of oEmbed, which is a set of advanced functions used by several popular providers such as YouTube, Vimeo and DailyMotion (and Twitter and Flickr too!).
See Embeds on the WordPress Codex for detailed oembed support information