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A person or company who wants to display on-line advertising - generally, at a cost.
A person or company who has ("publishes") a website (or some other form of on-line property) on which they wish to display on-line advertising (generally, from advertisers, and for a fee; but publishers do also display ads for free, either from advertisers, or to promote their own services when there are no paid ads to display).
In on-line advertising, and impression is a view, or an "opportunity to see" an ad. Every time an ad is displayed (rendered) on a website site or device, this is an "opportunity to see" the ad, and counts as an impression.
A click is whenever someone clicks on an ad. Click counts are sometimes filtered to prevent repeat clicks or other forms of fraud by publishers trying to raise revenues by repeatedly clicking on ads.
An acquisition or action is a certain (tracked) action that a user may perform after having either seen or clicked on an ad. Examples include purchasing a product, signing up to a newsletter, registering for a site, etc.
Cost Per Mille (from the Latin for "thousand") is the cost per 1,000 impressions (for the advertiser). For the publisher, this can also be thought of as the revenue per 1,000 impressions.
Cost Per Click is the cost per click (for the advertiser). For the publisher, this can also be thought of as the revenue per click.
Cost Per Acquisition is the cost per acquisition or action (for the advertiser) - that is, where the advertiser pays based the required action being performed after either clicking on an ad, or less commonly, after having seen an ad impression. For the publisher, this can also be thought of as the revenue per acquisition or action.
Effective Cost Per Mille is the effective cost per 1,000 impressions. By converting CPC and CPA rates back to an eCPM rate, campaigns of different cost models can be compared with each other to understand their relative performance. For the publisher, this can also be thought of as the effective revenue per 1,000 impressions.