Use the developer tools in your browser (i.e inspector in Chrome or firebug in Firefox) to see where the padding is coming from.

Either the padding is applied to something other than the body, or the padding is applied to the body but is still overriding your CSS. For example:

body.class {
    padding: 20px;
}

Would override your CSS. or

body {
    padding: 20px;
}

Declared after your CSS would still override.

Update:

Using developer tools you can see where the padding is applied to. The header padding is coming from the .container div, as you can see here:

The padding on the body is coming from 2 places, the .site-content div then the .container div, as you can see here:

How you remove (or reduce) this padding depends how you are editing the CSS. If you are working on the main style.css file then you need to change the CSS for .container on line 471 and .site-content on line 1265. You can see the file and line number of the CSS at the top right of the CSS in developer tools.

I can see the theme has custom CSS as well, so if you use that you need to add these to the custom CSS:

.container, .infinite-footer-container, .page-template-template-builder-php .entry-content > .twitter-share {
    padding: 0 10px;
}
.site-content {
    padding: 0;
}

Obviously change the padding to whatever you want it to be.

I hope that helps (and all makes sense).