Question on Google's Cost Per Impressions

Someone has been buying Google adword's CPM banners on one of my sites and I would like to have a better understanding on how they work.

I understand that with regular adsense, someone clicks on an ad and money is made, but if someone is using CPM instead of CPC, how is money made on the webmaster's end? Do I still get a profit if someone clicks on the CPM banners or do I only earn when I get a certain number of pageviews?

CPM is by pageviews

As Chris said, its by pageviews. As an advertiser I list a specific domain name I want to target and then big a CPM rate. So say I bid $10 CPM, and you give me 2456 impressions, I'll pay $24.56, you'll get whatevers left after Google's cut.

Clicks are not completely irrelevant here -- the advertiser might test out you inventory, and if no one clicks, may pull the ad campaign.