Dynamic Content for Google Sites

To embed web content or dynamic content within a Google Sites page, choose the Insert menu. Note that Google products are listed on the right. If you want to embed something not Google, choose More Gadgets:

Depending on the content you are embedding, you may have to do a search for the right Gadget. For example, clicking Public and typing Diigo in the search box produced:
If you cannot find a gadget specific for your content, Google does offer a generic gadget called Embed Gadget. Just search for "Embed Gadget" and see if your embed code will work with this gadget.