Keywords and/or Key phrases are what searchers type into their search engines to find your particular product or services. For example, if I wanted to find a Cosmetic Surgeon I would type "Cosmetic Surgeon" into my search engine and wait for the results to list.
The science behind SEO is matching what people think when they search with the content and keywords on your website. There's also the technical SEO science of how the content is structured and laid out on the page and also how it's embedded in the underlying source HTML that will ultimately determine your websites visibility.
Think of it like this - would you pay a sign writer to paint a very large sign and then have it placed on your roof facing the sun where no one could see it? Of course not! And websites are just the same - you must place your website in front of potential customers in order for them to find you - at that's where SEO comes in.
In conclusion, regular SEO maintenance will ensure you're getting the very best results for your advertising budget. You either pay to be at the top of the page position or you use SEO science to put you at the top, either way, you'll need a healthy mix of both Search Engine Optimisation and paid advertising if you want to be discovered.