Search engine optimization (SEO) is often referred to as if it is some single monolithic task. It's not.
SEO includes everything from the technical configuration of the server hosting a web site, to the site's coding and structure, to the visible content on the pages, to the development of incoming links to the site from other sites.
The server needs to be set up so that it properly serves 404 page-not-found HTTP responses for invalid requests. If Virtual Hosting is used, the Virtual Hosts must be defined and configured properly. Any redirects in the .htaccess or httpd.conf file need to serve the appropriate "file moved" response -- usually a 301 permanent redirect. Other directives in the configuration file must likewise be set up so as not to cause problems for the search engine spiders, or bots.
Keyword research needs be to done, to explore the range of possible keywords and phrases and their relative value for search targeting, taking into account the estimated number of searches, the level of difficulty in attempting to rank well for those searches, and the probable success of those searches in bringing targeted users to the site who are likely to turn into customers.
Titles must be custom-written for each page. The title must be optimized for the primary keywords the page is focused on, and must also be written with human marketing in mind, since the title is what appears as the bolded, clickable link in search engine results pages.
Visible content on the pages must be optimized for the search engine bots and for human visitors. Content must also be worthy of linking to. Link development is often viewed as "off-site optimization," but what's on the site is critical for this off-site optimization. You want links? Why should anyone link to you? Because of what your site offers, that's why.
Headlines and subheads are best presented as text, despite the aesthetic limitations inherent in HTML. Using CSS to style headlines helps there. Many sites do well using graphical images as headlines and including appropriate alt text for the image, or using technical methods to show the pretty graphical headline while feeding the text to search engine bots, but it's my opinion that nothing beats POT (plain old text) for all headings and subheadings on a page.
A good SEO professional understands all of these issues, and many more. Canonicalization issues. Duplicate content, and the appearance of duplicate content. Internal linking structures and practices that let the spiders know what the most important pages are on the site. Semantically correct code that uses h1, h2, and h3 tags appropriately for headlines.
One site may lend itself to SEO improvement by simply adjusting some of the underlying code, or the visible text on the page. Another site may require a complete overhaul to fix deeply entrenched problems. SEO is not an aftermarket add-on that you bolt on to your site after it's complete. Good on-page SEO is built into the site from the ground up.