Since heading tags typically make text contained in them larger than normal text on the page, this is a visual cue to users that this text is important and could help them understand something about the type of content underneath the heading text. Multiple heading sizes used in order create a hierarchical structure for your content, making it easier for users to navigate through your document.
Note that Google is pretty good these days at removing any special characters you have in your page title – and I would be wary of trying to make your title or Meta Description STAND OUT using special characters. That is not what Google wants, evidently, and they do give you a further chance to make your search snippet stand out with RICH SNIPPETS and SCHEMA mark-up.
The SEO starter guide describes much of what your SEO will do for you. Although you don't need to know this guide well yourself if you're hiring a professional to do the work for you, it is useful to be familiar with these techniques, so that you can be aware if an SEO wants to use a technique that is not recommended or, worse, strongly discouraged.