A commendation was an official award usually given as a formal statement of a heroic or monumental accomplishment.
While attending Starfleet Academy in the 2250s, James T. Kirk received a commendation for original thinking after he "changed the conditions" of the Kobayashi Maru scenario on his third try. (Star Trek II: The Wrath of Khan)
In 2371, Captain Janeway placed a special commendation in the logs of the USS Voyager for exemplary performance by The Doctor in his role as chief medical officer for successfully initiating first contact with photonic lifeforms and rescuing three endangered crew-members. (VOY: "Heroes and Demons")
The Order of the Bat'leth was the highest commendation a Klingon could receive. In 2373, Gul Dukat, added the cover names of Benjamin Sisko, Odo, Worf and Miles O'Brien (undercover as Klingon warriors) to the commendation list as part of an undercover operation to expose a Changeling in the Klingon leadership. (DS9: "Apocalypse Rising")
The Klingon High Council issued a commendation to the entire crew of the IKS Rotarran after their destruction of a Jem'Hadar starship and subsequent rescue of 35 Klingon warriors stranded in Dominion space in 2373. (DS9: "Soldiers of the Empire")