A principal investigator (PI) is the lead scientist or engineer for a particular well-defined science (or other research) project, such as a laboratory study or clinical trial. It is often used as a synonym for "head of the laboratory" or "research group leader ", not just for a particular study.
In the context of USA federal funding from agencies such as the NIH or the NSF, the PI is the person who takes direct responsibility for completion of a funded project, directing the research and reporting directly to the funding agency. For small projects (which might involve 1-5 people) the PI is typically the person who conceived of the investigation, but for larger projects the PI may be selected by a team to obtain the best strategic advantage for the project.
In the context of a clinical trial a PI may be an academic working with grants from NIH or other funding agencies, or may be effectively a contractor for a pharmaceutical company working on testing the safety and efficacy of new medicines.
Certification for principal investigator
The Association of Clinical Research Professionals (ACRP) provides a certification, specific to physician investigators/principal investigators (PIs). ACRP offers the designation "Certified Physician Investigator (CPI)".
In a study published by David Vulcano of Hospital Corporation of America, CPI certification has been shown to be a valid predictor of overall regulatory compliance based on comparing outcomes of FDA inspections between those that were CPI certified investigators to those that were not CPI certified. Specifically over the three year timeframe of the analysis, approximately 12% of FDA audits of investigators who were not CPI certified have resulted in an Official Action Indicated (OAI) classification, where there had been zero instances of OAI results among CPI certified investigators; this was statistically significant (p=<.001). Similarly, more than 50% of the inspections of CPI certified investigators yield No Action Indicated (NAI) results, compared to only 35% of investigators not certified by the Academy; this separation was also statistically significant (p=<.005). Other studies have had similar findings. Industry sponsors have considered CPI certification of investigators as an acceptable means of demonstrating competency in Good Clinical Practices 
- See e.g. NSF Grant Policy Manual 210f 'Definitions: Principal Investigator', available: http://www.nsf.gov/pubs/2002/nsf02151/gpm2.jsp#210; NIAID (NIH) 'Glossary of Funding and Policy Terms and Acronyms', available: http://www.niaid.nih.gov/ncn/glossary/default5.htm#pi
- Vulcano, David M. “CPI TM Certification as Predictor of Clinical Investigators’ Regulatory Compliance” Drug Information Journal January 2012 46: 84-87. http://intl-dij.sagepub.com/comtent/46/1/84.abstract
- Haeusler, Jean-Marc C. “Certification in good clinical practice and clinical trial quality: A retrospective analysis of protocol adherence in four multicenter trials in the USA“ Clinical Research and Regulatory Affairs, 2009; 26(1–2): 20–23.