A Court of Inquiry is an investigative body that meets to investigate some matter, including if civil or criminal charges against an individual or entity are warranted. The Federation Starfleet uses them to investigate matters concerning ships, installations, or personnel.
In 2355, after going to far in questioning Captain Jean-Luc Picard in his court martial for the loss of the USS Stargazer, then Commander Phillipa Louvois was reprimanded and informed that she would need to submit to a court of inquiry to determine if further charges were warranted. In response Louvois resigned from Starfleet. (TNG novel: The Buried Age)