Nakan memorial
A monument was an object set aside as a memorial to an event or person. Scanning for monuments was a way to discover if a planet had previously hosted a civilization. (TNG: "The Chase")
Monuments did not need to be physical objects, and the term could even be used abstractly. For example, a race of Ancient humanoids engineered humanoids to be a dominant life form as a monument to their existence. Gosheven described the colony on Tau Cygna V as a monument to everyone who had lived there. (TNG: "The Chase", "The Ensigns of Command").
In an alternate reality, Nelson's Column, a monument honoring Horatio Nelson existed in London. (Star Trek Into Darkness)
More informally, in 2372 Julian Bashir described the state of Miles O'Brien's quarters as a monument to his year as a bachelor. Similarly, in 2375, Ezri Dax, through her former personality Joran Dax, snarked that the crew quarters of Greta Vanderweg as a monument to bad taste. (DS9: "Accession", "Field of Fire").
Tom Paris once described his Paris Program Alpha-1 holoprogram as a monument to hundreds of hours he should have spent with B'Elanna Torres. (VOY: "Vis à Vis")
Figuratively, the term "monumental" could be used to describe particularly large works, or moments of particular historic significance. On Kataan, the construction of atmospheric condensers was considered a monumental task, and therefore unfeasible. (TNG: "The Inner Light") crewman Daniels described the Battle of Procyon V as a monumental moment in history. (ENT: "Azati Prime")
Specific monuments[]
On a Delta Quadrant planet inhabited Humans transplanted by Briori, a cryostasis chamber containing the 37's had become regarded as a monument. (VOY: "The 37's")
The Delta Quadrant planet Tarakis contained a monument to the Nakan massacre. (VOY: "Memorial")
By the 24th century, the whole area of the settlement where Zefram Cochrane originally built the Phoenix had become a national monument. (Star Trek: First Contact)
Gul Darhe'el was buried under one of the largest monuments on Cardassia Prime, a fact which Gul Dukat witnessed and offered as proof that Darhe'el was indeed dead when Aamin Marritza claimed to be him, alive and well. (DS9: "Duet")
After arranging for the Cardassian Union to join the Dominion in 2373, a monument to Gul Dukat was erected outside the gate to the Imperial Plaza on Cardassia Prime. (DS9: "By Inferno's Light")
In the late 24th century, Doctors Vellek, Jinaal Bix, Carmen Cho, Hitoroshi Kreel, and Marina Derex erected a stone monument to their colleague who had died while trying to access the Progenitors' life creation technology near the technology's control interface. It was later found in 3191 by Captain Michael Burnham and Moll and recognized as a monument to the fallen scientist by Burnham. (DIS: "Life, Itself")
In the 31st century, or at least the version of it from which temporal agent Daniels originated, Earth hosted a monument to the United Federation of Planets. The monument disappeared in a version of this future in which due to the Temporal Cold War the Federation did not exist. (ENT: "Shockwave, Part II")