CPI in online advertisement means Cost Per Install. Is a metric used to calculate the cost advertisers have for each App installed by the users who saw or who click in an Ad.
CPI is one of the most popular metrics in the APP world as it allows advertiser calculate and compare different traffic sources, different promotions, ads, etc. Normally is the metric that comes after the CPC. Before is the CPM.
Many agencies, ad platforms, and affiliates end up doing CPI campaigns and CPC campaigns as clients have a preference for this goal. It allows the clients to have a better overview and control of the costs.
CPI is like the CPL or CPA when compared to the display campaigns. Is just another name to define the cost for this specific action: the install.