Joshua Albert was a Starfleet Cadet assigned to the highly-regarded Nova Squadron. He was killed in 2368 during a flight training accident in orbit over Titan. While flying in close formation with four other Nova cadets - team leader Nicholas Locarno, Wesley Crusher, Sito Jaxa and Jean Hajar - Cadet Albert's ship collided with Cadet Hajar's, causing all ships to be destroyed. Albert was the only one unable to activate his emergency transporter in time.
Wesley Crusher and Joshua Albert were close friends. They both once went on skiing trip in Calgary, where Albert borrowed Crusher's sweater. Crusher had also helped Albert in his studies, especially in astrophysics and statistical mathematics.
In reality, Cadet Locarno had convinced the remaining cadets to provide false testimony and falsified flight plans during the inquiry. The crew of the Enterprise-D found inconsistencies in their testimony and their flight logs and correctly surmised that the five cadets were flying their vessels in a formation to ignite the plasma from their vessels' exhausts in an attempt to pull off a prohibited maneuver known as the Kolvoord Starburst.
On the final day of the inquiry, Cadet Crusher came forward and admitted that the true cause of the accident was that he and the other cadets pressured Albert in helping them attempt to perform the Kolvoord maneuver - partly vindicating Cadet Albert and giving his father some closure. (TNG: The First Duty)