Quality Score is a dynamic variable calculated for each of your keywords. It combines a variety of factors and measures how relevant your keyword is to your ad text and to a user's search query. If you need know how on Google Adwords, then follow the google adword lessons.
Quality Score is Google's measure of how much they want your advert to appear. It's based on relevancy, in the main part, but appeal to traffic and the quality (and trustworthiness) of your website are also important. In order to get a good Quality Score, you need your advert to be relevant to the search query. The most obvious way to achieve this is to put the keywords in your adverts. This can only be achieved if your keywords are grouped sensibly, of course. Your clickthrough rate is critical. If people click on your advert, Google thinks it must be relevant (and they know it'll generate more profit for them if they move it higher). They take your position into account, so you don't get a benefit from appearing higher (which will, of course, give you a higher clickthrough rate). Your website needs things like a privacy policy, and contact details, as well as plenty of relevant content. Why does your Quality Score matter? The better it is, the higher your advert appears for a given bid, or to put it another way, the less you have to pay to appear in the position that you want. For example, if my competitor has a Quality Score of 1.7, and I have a Quality Score of 3.4, then if he is bidding £1 per click, I only need to bid £0.50 to appear above him. Google explain it in more detail here: http://adwords.google.com/support/bin/answer.py?hl=en-uk&answer=10215
Not sure I would go as far as "critical". It is obviously of some importance (Google says so) but I do not feel there can be any hard and fast rule about CTR. Perhaps, it depends on the market or niche you are in but I have plenty of QS 9 or 10 keywords with very low, even non-existent, CTR. One of my most important keywords that always shows in pos.1 or sometimes 2 has a CTR of only about 0.5% yet still is QS10, while my keyword with highest CTR (from ave. pos.3) is only QS6. Personally, I think relevance of the keyword to ad text, display url and landing page content are far more important factors in QS.