Quality Score affects how your ad ranks (in both Search and Content) and it affects the minimum bid for your keyword. It's why I might pay five cents for a click on a keyword and you get charged twenty five cents on the same keyword.
There are (according to Google) over 100 factors that affect Quality Score, but the most important are:
Click through rate on Google
Overall history
Recent history
The copy in your ad
Your landing page (or destination page)
In addition, there's also another Quality Score attached to your account, that has to do with history and relevance. I think it's basically the sum total of all the keyword quality scores put together. When you put in a new campaign that Google doesn't know about (or use keywords that they don't have a lot of history about) they'll use your Account Quality Score to determine whether or not to give you the benefit of the doubt while they gather history.
Your keywords and ad text have to be very tightly focused, and your landing page has to be relevant, professional, and not look scammy or spammy or half-finished.
The whole idea is, Google wants people to trust their advertisers, and click on ads and buy things (which spurs advertisers to spend more on ads) Users won't do that if they click on the ad and then immediately fly away because the landing page doesn't look trustworthy, or relevant, or the ad was misleading, or whatever.
You didn't mention how new your account / campaign is. On a brand new account and campaign, you are almost ALWAYS going to see your keyword minimum bids jacked way up, while Google gathers history on you and your keywords.
If this is a new account and/or campaign, I would suggest you pick out one or two keywords, and leave them at Google's minimum. Control your costs with the daily budget - even if it means you'll only get a couple of clicks per day. But this is the only way you'll work your way up and gain trust. If your landing page is good, and your ads are good, then you will see your minimum bids start to go down.
In my experience(
*) it takes at least two weeks to a month for a new campaign without stellar account history to start seeing its minimum bids go down. Sometimes longer. You have to be patient.
You can view your Quality Score and Minimum Bids in the AdWords console (you have to turn it on in the Keyword view)
More information here:
http://adwords.google.com/support/bin/answer.py?hl=en&answer=21388
(*) My experience consists of managing a combined $70k/mo spend with AdWords since 2002, and I'm a twice over GAP (Certified Google AdWords Professional)