What is the origin of the word "Impression" in the Internet advertising term "Cost-Per-Impression" (CPM)
Solution 1:
It is a continuation of usage from the legacy (print) advertising. An impression is a single publication of an advertisement, derived from the platen making an impression on paper in the letter press system.
It is not related to the impression it makes on the viewer/ user/ potential customer.
Solution 2:
There is an unfortunate error in the original question. "Cost Per Impression" is not "CPM", as if "M" is a phonetic abbreviation for "impression". The "M" is "thousand" so "CPM" is "Cost Per Thousand", with the "impressions" implied.
In advertising, CPM is often the billing unit, CPI is rarely if ever used, and this applies to print as well as internet. If you book an ad campaign for your car or scotch to be in every Conde-Nast publication in the US, your billing will be based on the total number of magazines sold (or maybe printed, as in the original meaning of "impression"), regardless of the circulation of the individual magazine titles.