The process for embedding widgets on a SquareSpace website is a bit different than most website editors.
First, insert a code content block, like so -
Make sure the "HTML" type is picked on the right, and uncheck the "Display Source" box. Paste both the <script> tag and the <div> code you have in your account for the widget you're embedding -
Click on "Apply" on the bottom right of the dialog box. The content area will show "Scripts disabled" - that's fine. Click on "Done" and "save" in the top-left corner - it should now render the widget on the page.