The Starfleet bridge officer examination is a series of tests for Starfleet officers who wish to be able to take command, besides the command officers such as Captain, First Officer, and Second officer. The test has many stages, but the final exam requires the officer to make a choice that sends one person under their direct command to certain death. No one who fails the test can serve as a command officer on the bridge of a starship except in emergency situations.
In 2370, after attending her Starfleet Academy reunion, Deanna Troi felt she was one of the few classmates who hadn't risen to command level status. This combined with the bitter memory of how badly she acted under pressure two years earlier when the Enterprise hit a quantum filament, led her to talk to Commander Beverly Crusher. Crusher, who takes the night watch of the bridge, tells her that she took the exam in 2362 when she wanted to contribute more than just in sickbay. (TNG: "Disaster")
This led Deanna to try the test, which Commander Riker administered. The final portion of the test, which also included a question and answer portion, was to make decisions in a holodeck simulation. In it, the officer is required to ask an officer to sacrifice themself to save the ship. She had failed the final exam several times before realizing that its purpose was to ascertain whether or not she would be able to send a subordinate to certain death. Afterwards she passed the exam, and was promoted to Commander. (TNG: "Thine Own Self")