A reprimand, in Starfleet, is a serious formal censure that is included in a person's service record. A commanding officer can reprimand a member of Starfleet for violations of the law, regulations, or other unwarranted behavior on the part of the crew member. A reprimand can have a serious negative effect on a person's career, such as slowing or even stopping their upward movement through the chain of command, making them ineligible for certain positions, or demotion to a lower rank.
When Demora Sulu was apparently killed by Captain John Harriman, her godfather Pavel Chekov was quite angry with Harriman for her death. After her funeral service Chekov proceeded to get into a fight with Harriman. In the aftermath of their quarrel, a disciplinary board entered a formal reprimand in Chekov's service record, and ordered him to make a written apology to Captain Harriman. It was later revealed that it was not Demora who died, but a mindless clone created by an old enemy of her father Hikaru Sulu. The reprimand meant that it would be a number of years before Chekov would gain his own command. (TOS novel The Captain's Daughter).
Captain Jean-Luc Picard would be forced to enter a reprimand in Lieutenant Worf's record after Worf killed Duras, son of Ja'rod. This was in response to Duras murdering K'Ehleyr, and the Klingon Empire felt that Worf had acted within the bounds of Klingon law and tradition. However Captain Picard felt that he could not condone such killing by anyone wearing the uniform, and entered a reprimand in Worf's record. (TNG episode Reunion and Startrek.com Biography of Worf)
Starfleet Intelligence later entered another reprimand in Worf's record when he abandoned a mission to retrieve his critically injured wife Jadzia Dax. This resuled in the death of a Cardassian defector with valuable intelligence on Founder activities in the Alpha Quadrant. Because of the covert nature of the mission, no formal charges were filed, but Captain Sisko believed that Worf would have a hard time ever gaining his own command. (DS9 episode Change of Heart and Startrek.com Biography of Worf)