Flickr is, to be honest, looking a bit long in the tooth, although its recent innovation of displaying very high resolution photographs by default is, shall we say, striking. But it is still a great service in my opinion, and for the writer a much better one than, say, Facebook.
You've almost certainly already seen examples of embedding. Go to any website where there's a video clip on the page, and you're looking at it in action. In other words, embedding is simply the act of inserting code into a web page or blog that puts the object right there on the page. This 'object' might be a video, a presentation, a document, a picture -- just about anything, in fact.