What is oEmbed? 
To quote https://oembed.com:
oEmbed is a format for allowing an embedded representation of a URL on third party sites. The simple API allows a website to display embedded content (such as photos or videos) when a user posts a link to that resource, without having to parse the resource directly.
FastComments supports the oEmbed format and is available through products that use https://embed.ly.
Creating an oEmbed Conversation
With FastComments, a conversation has to be first created before it can be embedded.
To do so, simply visit fastcomments.com/create.
Once choosing a name, a secure link will be created.
This link can be visited and used as its own chat. Or, it can be provided directly to an application that supports oEmbed, or https://embed.ly, to insert the conversation.
Embedded conversations can be customized just like any other FastComments installation using the Customization UI. Read about customizing the comment widget here.