Have you ever struggled to embed external media in a web page? So many providers to choose from...youtube, vimeo, soundcloud, mixcloud, just to name a very few, and they all have completely different URL structures, different players, different...everything.
The aim of the game is to be able to take, say, a standard SoundCloud URL and paste it in to your page, and have the page somehow turn it in to embedded media.
Step forward oEmbed. This is a new, informal "standard" starting to be adopted by a lot of providers.
The theory is simple - the provider creates an oEmbed webservice, eg http://soundcloud.com/oembed, which when tickled with a request containing a standard URL of that provider, returns a JSON object containing much well-defined meta-data about the media in question.
Lots of info on the format of the request you make and the data returned can be found at http://oembed.com/
The bit you need to know for embedding is that the "html" property in the response will contain the provider's embed code for this media. Append this to your document somewhere and you're done.
And a provider is expected to support JSONP (Otherwise it wouldn't work cross-domain).