In SharePoint 2013 admins can now Insert an iframe element into an HTML field like Content editor webpat on a page. This will let users Embed dynamic content from other sites, such as videos or map directions on any SharePoint site page. Any external domains that will be Inserted in Iframe should be added as approved domains in "HTML Field Security". By default, certain trusted external domains are already approved for use in iframes.Site collection administrators can customize the field security settings by changing the default trusted external domains.

An example taken from LearningSharePoint.com.

To add a Youtube Video add the "Youtube.com" Domain in "HTML Field Security" first.
Lets look at the Steps -

1. Navigate to Site Settings (top-level Site collection) -> HTML Field Security.

2. Make sure the domain "Youtube.com" is added as permitted domain.

3. Navigate to your Youtube video and click on Share and then Embed.

Copy the highlighted text.

4. Add a Content editor webpart on a page and then click on "Edit Source" in "Format Text" tab in Ribbon. Add the following in the Source. <iframe width="420" height="315" src="http://www.youtube.com/embed/hyRLzUVw4Vw" frameborder="0" allowfullscreen></iframe> and click ok. Result -