An annual event held by the schoolchildren of the Enterprise-D, who make pictures and models of their captain for a contest that an embarrassed Picard has to judge.
Captain Picard Day is a yearly celebration organised by the children who live aboard the USS Enterprise-D. They produce drawings, paintings and sculptures of the captain, and Picard, who is famously ill at ease with children, is expected to choose a winner.
It opens The Next Generation episode The Pegasus. Picard glumly surveys the entries in his ready room with Troi, who reminds him that he is a role model, and Riker, who seizes on a doll of the captain and gives it a voice. A call from Admiral Blackwell interrupts, and Picard has to explain the banner behind him.
The banner turns up again in the first episode of Star Trek: Picard, kept among the mementoes in his archive at Starfleet. Lower Decks echoes it with a Captain Freeman Day aboard the Cerritos.