A post click cookie is a cookie used for tracking actions undertaken by users on the advertiser’s website after a click on an ad bought by this advertiser. Post click cookies are mainly used for tracking conversions.
The marketing vendor - Google AdWords, an ad network, an ad exchange, a retargeter, an affiliate platform, etc - places a cookie on the computers of web users who have clicked on ads. Then, the vendor make available to the advertiser a conversion tracking tag or code to be placed on the "thank you page" or confirmation page following the conversion. When a conversion occurs, the conversion tracking code allows the marketing vendor servers to access the buyer’s hard disk to look for an eventual post click cookie. If a post click cookie is found, the sale is attributed to the ad that has been clicked through.
Post click cookies have often a 30 days lifetime and sometimes longer. It allows marketer to attribute the sale to the ad even if the sale is not completed on the first visit after the initial click through.
From a technical point of view, post click cookies are often considered as first party cookie as they are placed when the user is redirected by the advertising platform.