The plaque commonly displays the name of the ship, as well as its class and shipyard of origin. Many more recent plaques also display the ship's official motto, plus a list of notable Starfleet officers involved in the assembly of the vessel.
In real life, the list of "officers" is actually a list of notable production staff members from the various television sets. "Admiral" Gene Roddenberry is commonly listed as the Starfleet Chief of Staff.
After earlier being made to wait for quite some time by the Sheliak, Captain Picard took his time answering their hail, inspecting the ship's dedication plaque in 2366. (TNG: "The Ensigns of Command")
In 2368, after having their memories temporarily submerged, the senior staff of the Enterprise-D read the ship's dedication plaque to figure out the name of the ship. (TNG: "Conundrum")
When USS Voyager found the USS Equinox in 2376, CaptainJaneway noted that the Equinox's plaque had fallen, and they should hang it back up. Similarly, after days of battling with the Equinox after they betrayed the Voyager crew, Voyager's dedication plaque fell down. Chakotay and Janeway noted that after years of battles, it had never fallen down before, and in a symbolic gesture, they put it back "where it belonged." (VOY: "Equinox", "Equinox, Part II")
In the non-canonStar Trek: Titan premier novel, Captain Riker has a tough time selecting a proper quote for the Titan's dedication plaque. (It has never been implied one way or the other if it is standard procedure for a ship's captain to choose the quote on their own ship's plaque.)