What is Cost per Action?

Cost Per Action is an online advertising pricing model, where the advertiser pays for each specified action (a purchase, a form submission, and so on) linked to the advertisement. The CPA can be determined by different factors, depending where the online advertising inventory is being purchased.

Most CPA offers by advertisers are about acquiring something (typically new customers by making sales). 
In CPA campaigns, the advertiser typically pays for a completed sale involving a credit card transaction. Cost per action is a means of controlling advertising spend. CPA also offers an opportunity to control ROI.

CPA and affiliate marketing campaigns are publisher-centric. CPA campaigns are usually low volume and complex. Typically, a consumer has to submit credit card and other detailed information. It is an important bidding option if looking to ensure that a campaign receives the optimized number of conversions in exchange for advertising spend.

This can also be done through Call Tracking whereby an advertiser has several phone numbers assigned to various ad campaigns. The advertiser is able to then track which advertisements are getting the most attention by quantifying the number of calls per ad.

References

Wikipedia
Wordstream