I've used Adwords and Adwords Express for a long time, even went through their certifications and became a Partner (only after I sold enough Ads). That being said, I have a bone to pick with Google, and it seems I'm not the only one.
What is Adwords? Adwords is Google's Pay Per Click program, where you can buy keywords and get your ad on the top of the search results for that word or phrase. You can have a text or image ad, and the cost per click is determined by an auction-type system, where businesses compete with each other, while Google makes all the money.