This is definitely something we have discussed supporting. I have sponsored the feature on our Trello Board, as I too would like this ability. https://trello.com/c/Qf0BxQEt
Please up-vote and add your comments to the card on how you would be using entry embedding and what particular functions you would like to see in the feature.
For now, there are a couple of ways you can accomplish getting the data into your website, they just take a little bit more work and know-how.
The first is using our "Post JSON data to website" feature. By writing a custom webhook, you would be able to retrieve your entry data and display it on your site. For more information on this method, read our blog post: https://www.cognitoforms.com/support/66/data-integration/webhooks.
The second method would be to use our recently released Zapier integration. Here, again, you can use the Webhook, or many other options that Zapier offers, such as having the data sent to a SQL or MySQL database. Read more about our Zapier integration here: http://blog.cognitoapps.com/connect-your-cognito-forms-to-almost-anything-with-zapier