A Key Performance Indicator (KPI) is, to put it quite simply, an indicator. It indicates whether and how efficiently a predefined and agreed upon goal is being achieved; is the current state of affairs acceptable with regards to the predefined benchmarks and/or limits. Organizations use KPIs to constantly monitor performance, stay focused, raise flags and take corrective actions well within time.
KPIs vary in their nature, from progress to quality to conformance and are determinate tools indicating how well specific goals are being achieved. They are generally formulated and agreed upon in the early stages of the project.
Different organizations lay emphasis on different aspects of project performance. Different projects, clients, circumstances also dictate different parameters. Some common indicators / benchmarks are;
Productivity and cycle times,
Percentage overshoot over planned duration,
Percentage variance from planned completion,
Required minimum periodic rate of progress,
As can be seen, I am partial towards progress indicators. However, the much broader horizon includes others such as number of milestones missed, resource utilization, NCRs, Return on Investment, Profitability, defect rate, quality, and many, many more. Any combination of these can be used as a project health/performance dashboard.