Quality Score is central to the Google Adwords system. Here is what they have to say about the Quality Score:

Quality Score for Google and the search network is a dynamic metric assigned to each of your keywords. It’s calculated using a variety of factors and measures how relevant your keyword is to your ad group and to a user’s search query. The higher a keyword’s Quality Score, the lower its cost-per-clicks (CPCs) and the better its ad position.

Quality Score for any keyword on Google and the Search network is calculated based on the historical clickthrough rate (CTC) of the keyword and the matched ad, your account history, the historical CTR of the display URL in the ad group, landing page quality, keyword relevance to the ad in its ad group, relevance to the query of the ad text and the keyword, your account’s performance in the geographical region where the ad will be shown and few other factors.

High Quality Score not only saves you money but also gives your ad higher visibility (As it appears higher). IT also is an indication of how successful your ad will be (conversion rate).

Here are some tips to go about improving your Adwords Quality Score:

Organize your campaigns such that each product and service has its own campaign (e.g. if you offer several products like ecommerce tools, cms systems, social networking scripts then you might want to create a campaign for each of them and same for services)
Here I am going to talk about keywords targeted adgroups only. Within a campaign you can create several adgroups and associate keywords with them. In order to achieve high adwords quality score, create adgroups of very closely related keywords. The way to go about it to decide on root/common keyword for the adgroup and all keywords in that adgroup should have that term as a common/root term, e.g. let us say we decide to use “software development” as the adgroup root term then we should have keywords like “custom software development”, “software development India”, “best software development” etc in that adgroup (Note: you can decide to choose “software development India” as your adgroup root term and have keywords all other keywords based on that, the decision is upto you and will depend on how granular your targeting needs to be) [NOTE: Google Adwords Editor has a pretty decent keyword grouping tool, download and try the editor.]
The ad copy you write for that adgroup should include atleast the root term.
To start with you can create multiple ads and turn off ad optimization so all of them are rendered equally. After a week or so you can pick which ones work best for you and stop the others or write more ads based on what you see seems to be working.
Experiment with the “match type”: exact, phrase, broad to see which one gives you best quality score and lower cost per click.
Landing page is crucial not only from conversion point of view but also from the point of view of saving money on your campaign by ensuring you score high on quality score for them. Few high level things to keep in mind for the landing page design are: provide relevant, unique and substantial content on your landing pages.
Create an about us page and link it to the landing page
Create a privacy policy page and link it to the landing page
If you have enough time and are working on a long term campaign, it might be worthwhile to create a sub-site for the PPC campaign
Put relevant content, link to related content pages and provide details on refund and returns. It might be worthwhile to mention your no-spam policy.

Improving Ad Rank

Remember, the better your ads, the less you will pay per click. Focus on these things to get clicks at the best value.

Google also factors in the historical performance of your adwords account in its quality score calculations. Sometimes you might be better off with a new account if the earlier one is already messed up by someone.

Check out this video with Google Chief Economist Hal Varian for more info: