There are two kinds of search results: organic and Pay-Per-Click.

Pay-Per-Click or PPC results are the sponsored ads shown along with the organic search results. With PPC Advertising, you generally bid for keyword terms and your ads (sponsored results) show up in designated areas on the page. Your ad will be shown in shaded boxes above or to the right of the organics results. The higher you bid for the keyword, the higher your ad is listed.

Organic results generally show up as ten or so results per page and appear as the bulk of the content on the page. These results are gathered by search engines’ web crawlers (robots) and ranked according to the gazillion lines of code algorithm that the engineers of the company have developed over the life of the search engine company. This algorithm evolves constantly so it important to use strong time tested methods to keep you near the top.

Lets look at an example:
Lets say you sell "giant purple unicorn tshirts". In doing your research, you find out that if you go the PPC route you can expect to pay the following:

tshirts = $1-$3 per click
giant unicorn tshirts = $.25-$.35 per click
purple unicorn tshirts = $.15-$.25 per click
unicorn tshirts = $.50-$.75 per click
giant purple unicorn tshirts = $.05-$.15 per click
giant tshirts = $.80-$1 per click

As you can see, in our example, its actually cheaper to go after the more specific terms. However, there will be less traffic for a 3 or 4 word term then there will be for a 1 word term. So you will need to constantly monitor your terms, the costs, your campaigns, your Click-Through-Rates (CTRs), your account balance, and your Return-On-Investment (ROI).

If you can get your web site to show up within the organic search results for any of these same terms, you do not need to worry about monitoring changing costs. Statistics also show that the majority of clicks for a term are performed on the first 5 organic results. The potential for click through is much larger with organic results than it is for PPC results.

My advice... Use PPC for short to medium term campaigns (weeks to months) and organic for longer term campaigns (years).