Hi there,
Historically in SEO, search engines used to use the 'exact match' text of a page (be that in the page title, URL, page copy, H1 etc.) to inform the term to rank the page for.
Nowadays, Google is a lot more understanding of related terms and synonyms since the 'Hummingbird' update. For example, if I optimised my entire site for 'advertising agency', there's a good chance that Google will understand that 'branding' is likely to come under my field of expertise and rank me for searches such as 'branding agency' or similar.
Their optimisation for the term 'branding agency' might not just be down to the homepage - the likelihood is that they have a page on the site explaining their branding services which helps the overall domain rank for that kind of term.
I hope this helps,
Sean