Todays search engines analyze the textural content of pages, and tries to determine the uniqueness of the content, in relation to whatever search string was entered.
Keyphrases are two or more words put together to form a keyphrase, such phrases are usually much easier to optimize then the individual keyword.
Keyword analysis and Density
The keyword density has little to do with how a page ranks. Of cause you should mention the keyword, or keyphrase at least a few times throughout your content, but anything beyond that is likely to have a negative effect.
There are many factors which determines how a page should rank, one of the hardest to overcome is competing pages. While the density of keywords can impact you negatively, it has little to do with competing sites outranking you.
Some of these sites are well established, and have many incoming links to help them achieve a good placement. Their individual page might not have that many links, but authority can also flow from the main domain, down to the deeper pages, (given that they are linked internally of cause.)
Say you where to find a keyphrase often used by searchers, like "very unique keyphrase", and there where no pages with that exact title match, then you may very well have a top 5 ranking spot just waiting for you to make a page on the subject.
Uniqueness of Content
The uniqueness of your content is something which is far more important then keyword density. If one of your pages doesn't rank high enough for certain search phrases, then try to look into what you can do to improve said page. One way to do that, is to change a non-matching title, to a title matching the exact keyphrase used by searchers.
Also, try to cover more subjects to make your content appear more unique, as they say: content is king. Covering multiple closely related subject on the same page, is likely to increase the uniqueness of your content a lot.
Many online shops don't understand this, so their individual product pages might not even rank on the first page at all, while often they could achieve a top 10 placement with just a little effort put into writing content.
Think about the Keyphrases on your page
As mentioned earlier, Keyphrases are far more important then individual Keywords. Have you actually included the phrases on your page, that people would be using when searching? A lot of website owners totally overlook this, making their sites perform really badly in the search engines.
Think about the phrases that you use on the site, for instance, if people are searching for "SEO Tutorial" to find the SEO Tutorial on Brugbart, then it would be a good idea for us to include the phrase somewhere in the content on that page.
Some webmasters also include "lists" of phrases and words on their pages, don't do this. Its useless to your users, and will just make your pages appear more like spam. Instead try to include potential search phrases more naturally, in a way that its also useful for users. If a site looks like spam to a user, they will surely also be less likely to link to that site.
Compare your content to competitors
It can also be useful to compare Competing pages, with the pages on your own site. I.e. Do the competing pages include actual keyphrases? If they don't, then you could sometimes easily outrank them, by simply including keyphrases on your own pages.
You could also check to see if your competitors have exact title matches for their pages, which often isn't the case. Simply changing your page titles, to exact matches to certain keyphrases, can give you a boost when people are using those keyphrases.
It may also be somewhat beneficial to include the main keyword or keyphrase in the description meta tag, but if this does anything, then its likely to be of little actual value.